After half hour it appeared to be another fruitless trip to West Yorkshire and the John Smith's Stadium for Albion.
The Baggies found themselves 2-0 down to some brilliance from Terriers' Chelsea loan star Tino Anjorin, who scored a fine opener and a second that left a lot to be desired from an Albion perspective.
But Wallace pulled one back before half-time as Huddersfield showed some defensive nerves of their own and, following an underwhelming first half Steve Bruce's side were much the better side in a frantic second period.
Wallace levelled it up with his second, a thumping volley before the hour and Albion were on top for almost the entirety of the final half hour, which included Grady Diangana firing a fraction wide and busy keeper Lee Nicholls saving from Karlan Grant.
But the outstanding talking point will be referee Andy Davies' decision not to award a penalty for Will Boyle's sliding challenge on Grant inside the final 10 minutes - which left Bruce, his staff and players furious and earned the Baggies boss a booking for protesting.
Albion had to survive a let off or two at the other end, notably as Josh Ruffels struck a post, but a point was the least they deserved. The winless league run in Huddersfield, dating back to Jordao and Lee Hughes efforts in 2000, goes on.
And, with the transfer window shutting in five days, there is much work to do for Albion and Bruce, whose lack of depth was highlighted once more in another matchday squad.
The Baggies have mostly been defensively sound this term but they were carved open and scored against too easily in the first half in Yorkshire - but their spirit and character to fight back and earn a point, with some relentless attacking, does at least show some promise.
Albion, unsurprisingly, named the same starting XI as in their last league encounter - last weekend's 5-2 home hammering of Hull.
Dara O'Shea, made captain again by Bruce, was the only player to feature in Tuesday's disappointing Carabao Cup exit at Derby to remain in the side.
The headline omission from the visitors' matchday squad was that of Matty Phillips, who was not included among the substitutes. Bruce had mentioned there were no injury concerns 24 hours earlier.
Teenager Tom Fellows, of the Baggies academy, took his place on the bench.
The hosts, under head coach Danny Schofield after Carlos Corberan's summer resignation, started the day third-bottom following three defeats from their opening four league games.
The Terries boss made three changes, two of which were enforced with skipper Jonathan Hogg injured and Tom Lees suspended. Anjorin, Jon Russell and Rarmani Edmonds-Green came into their side.
It was a low-key opening 10 minutes but Huddersfield were the brighter of the two sides.
Chelsea loanee Anjorin, an England under-20 international in his second loan spell with Town, looked particularly sharp and forced an early set-piece following a powerful drive.
Albion conceded a needless second corner as Darnell Furlong helped behind under little pressure and it was from there that the hosts opened the scoring.
Bruce's men did not respond to a short corner work out to Anjorin who from all of 25 yards and out to the left, send a brilliant strike full of bend and dip into the far top corner over David Button, in front of the travelling Baggies.
To their credit Albion responded well to the setback and began to settle with the ball and force better positions, though there was a feeling of lethargy early on.
John Swift shot well over in trying to recreate Anjorin's brilliance before Okay Yokuslu helped tamely at goalkeeper Nicholls from a Wallace cross.
Albion tried to up the ante and the contest had just passed 20 minutes when Nicholls made a fantastic reaction save to keep out Yokuslu, who managed good contact inside the box from another Wallace cross from the right. The Turk thought his effort was in before the keeper's intervention.
Huddersfield threatened as captain O'Shea blocked from Anjorin and Ollie Turton headed the resulting corner wide.
The visitors continued to push and Nicholls was at his best again to deny Grant, who was picked out at close-range from Wallace. The striker found the keeper right at his feet and was unable to lift his finish over Nicholls as another good chance went.
And Bruce's team were made to pay on half hour as they found themselves two goals down as Anjorin struck once more.
The Terriers flashed from one end to the other in devastated fashion. Grant wanted a penalty after trying to connect to a Grady Diangana cross but the home side quickly escaped their own half.
O'Shea appeared to be winning the race to the ball out on the right touchline but hit the deck under light contact and slid off the pitch appealing for a foul.
Referee Andy Davies waved play on and Anjorin found himself in the box, in space, from something of an angle, but he made light work of that and finished easily at the near post high above Button's efforts. It was a poor goal to concede.
Albion were shocked. They tried to reply as the busy Wallace flicked wide, but did manage to pull one back eight minutes before the end of first half.
The goal consisted of involvement between Albion's star attackers Wallace, Swift and Diangana. Wallace fed Diangana on the left of the penalty box and the winger turned his defender inside out, before a low cross found Wallace in lots of space to coolly slot in under Nicholls.
It was a vital time to pull one back and Huddersfield were happy to see out the first half with a couple of injury stoppages. The hosts had been, much like Albion, suspect defensively themselves and some jitters entered the locals.
Albion started the second half, in which they were attacking the end of their loud away following, on the front foot. The travelling Baggies did their bit to inspire the side.
It worked. The second half was just 12 minutes home as the boisterous away end erupted after the electric Wallace's brilliant second.
The Baggies worked it left to right and Swift beat his defender to a bouncing ball on the edge of the box, where he cushioned a flick over the Terrier's head into the path of Wallace inside the box.
The former Millwall man arrived in perfect time to crash a thumping volley high to Nicholls' left for a brilliant equaliser.
It was all Albion and the visitors forced a flurry of chances after the hour as they were left wondering how it remained level.
Yokuslu spooned haplessly wide with his left foot when Swift might have taken the effort on but a big opening came the way of Grant, who was once more denied by Nicholls from an acute left angle after being played through by Conor Townsend.
The resulting corner was only half cleared and it dropped to Diangana on the of the box. He crashed a brilliant volley which spun just inches wide of goal off the outside of his left foot.
The ball looked set to crash into the corner from the view in the press box.
Albion kept knocking on the door as Furlong headed over as Bruce instructed his stoops to push high and wide.
Home boss Schofield made his second change with 20 minutes left as the Terriers went 4-4-2 to try to wrestle back any form of control.
The Terriers made a rare foray into Albion's half and, having forced a couple of corners went mightily close to finding an unlikely winner as somehow a goalmouth scramble stayed out.
Seconds later, down the other end, Albion should have been the side ahead. Furlong checked on to his left and a lovely cross picked out Yokuslu, effectively unmarked, and his header was sent well over. Bruce turned away as the clear chance went.
Bruce sent Robinson on for Molumby in an attacking switch as the contest entered its final 10 minutes.
A frenetic finale was to follow. Albion were fortunate with five minutes to go to see Terriers sub Jordan Rhodes' header drops narrowly wide of the left post.
Moments later and the visitors were apoplectic with rage as a huge penalty decision went against them.
Grant was played inside the box and raced to meet the ball with Will Boyle, who slid in. The defender brought down Grant and the Albion players in red and Bruce and his coaching staff surrounded the officials appealing for a spot-kick.
Replays looked like the defender had through Grant to bring the frontman down. Bruce was livid and booked for his protestations.
It was nearly much worse for the Baggies seconds later as Huddersfield left wing-back Ruffels crashed an effort against the post from distance, the rebound was well blocked.
There was to be no winner at either end in a frenetic contest that might have gone either way. Albion would have taken a point at 2-0 and had to settle for as much.
Huddersfield Town (3-4-3): Nicholls; Turton, Nakayama, Edmonds-Green (Boyle, 83); Kesler-Hayden, Russell (Rhodes, 83), Rudoni, Ruffels; Thomas, Ward (Camara, 72), Anjorin (Holmes, 59).
Subs not used: Chapman, Mahoney, Jackson.
Albion (4-2-3-1): Button; Furlong (Gardner-Hickman, 85), Ajayi, O’Shea, Townsend; Yokuslu, Molumby (Robinson, 82); Wallace, Swift, Diangana; Grant.
Subs not used: Palmer, Bartley, Livermore, Reach, Fellows.
Attendance: 18,696 (1,624 Albion fans).
Referee: Andy Davies