Valerien Ismael's side headed to Lancashire having lost their last four games on the road.
But while they put an end to that losing streak, they were unable to find the win they craved - and their performance deserved - at Bloomfield Road.
After a fairly even opening half-hour, the Baggies really turned the screw with Karlan Grant, Matt Clarke and Jordan Hugill all having excellent chances to earn all three points for Ismael's side.
Blackpool also had their moments - with England international Sam Johnstone making an outstanding double save in the first-half stoppage time.
But this was a game Albion really should have won - with fans showing their frustration at the full-time whistle with chants of 'sack the board.'
Ismael opted to make two changes from the team that was beaten at Huddersfield when naming his starting line-up.
With skipper Jake Livermore suspended after picking up a red card in Yorkshire, Jayson Molumby returned to the side in central midfield where he partnered Alex Mowatt.
There was also a change at right wing-back where Darnell Furlong came in for Taylor Gardner Hickman.
Otherwise, Ismael opted to keep faith with the team that had struggled at the John Smith's Stadium.
In the head coach's 3-4-3 formation, Matt Phillips continued to play as a central striker with Grady Diangana on the right flank and Karlan Grant on the left.
Blackpool lined up in a traditional 4-4-2 formation with Shayne Lavery and Gary Madine their front two - Josh Bowler and Keshi Anderson were the widemen.
In what was an entertaining opening 20 minutes, both teams looked lively whenever in possession.
And they were each presented with chances to open the scoring due to goalkeeper errors.
It was Albion who threatened first when Dan Grimshaw inexplicably passed the ball straight to Diangana who was well placed just outside the box.
The forward, though, didn't seem to realise just how much time he had and fired well wide when he should have done better.
A few minutes later it was Sam Johnstone who was struggling with his kicking.
Following a back-pass that may have bobbled, the keeper sent a poor kick straight to Bowler.
And he managed to find Lavery in the box who stabbed the ball at goal only for Johnstone to get back and make a simple save.
Playing in their 4-4-2 formation, Blackpool were being a lot more positive on the ball than the vast majority of sides Albion have faced this season.
But after an even opening half-hour, the Baggies really started to turn the screw.
A brilliant pass from Phillips sent Conor Townsend charging into the box - with the wing-back then seeing a low drive blocked by Grimshaw.
Ismael's men then went even closer when Diangana slipped Grant in on goal.
The forward looked to slide the ball across goal and into the corner but Grimshaw made an excellent stop with his legs to keep the ball out.
Albion continued to charge forward with Phillips, in particular, knitting their play together well.
But despite their dominance, they were unable to find that final bit of quality.
And they had Johnstone to thank for going in at the break on level terms - with goalkeeper producing an outstanding double save just seconds before the interval.
Following a long throw, Madine acrobatically turned the ball towards goal with Johnstone making an excellent, one-handed stop, to keep it out.
But the ball then fell for Anderson who looked destined to simply nod it into an empty net.
Incredibly, though, Johnstone managed to get himself back up and across his goal to make a second brilliant stop.
It was the hosts who created the first-chance following the re-start.
Anderson went past Cedric Kipre too easily before picking out Madine with a cross.
The striker really should have moved the ball on again but instead saw a shot from eight yards blocked by Kyle Bartley.
Overall, though, it was Alboin who being the more aggressive of the two teams.
And they had two glorious chances to get themselves ahead just past the hour mark.
First, Matt Clarke rose highest to meet a corner only to send a header inches over the bar.
Substitutes Callum Robinson and Jordan Hugill then combined in the box - with Robinson squaring for Hugill who was centrally placed eight yards out.
The striker looked to side-foot the ball home but his effort took a deflection before sailing wide of the post.
Ismael's men were now pilling on the pressure.
But on a rare foray forward, Blackpool almost got their noses in front when Anderson slipped in CJ Hamilton.
He, though, turned the ball over the bar when he really should have hit the target.
For the final 10 minutes, it was backs to the wall stuff for hosts.
Following a scramble, Clarke saw a volley claimed by the keeper.
Grant was then unable to turn a dangerous Townsend cross towards goal
And those misses ensured Blackpool held on for a point - much to the frustration of the travelling Albion fans.
Albion (3-4-3): Johnstone, Kipre, Bartley, Clarke, Furlong, Molumby, Mowatt, Townsend, Diangana (Robinson 61), Phillips (Hugill 61), Grant.
Subs not used: Button, Ajayi, Gardner-Hickman, Reach, Fellows.
Blackpool (5-4-1): Grimshaw, Gabriel, Ekpoteta, Husband, James, Wintle, Dougall, Bowler (Dale 66), Anderson, Lavery (Hamilton 66), Madine.
Subs not used: Moore, Connolly, Yates, Gretarsson, Sterling.