Although the hosts gave Blackburn two goals at either end of a half that yielded five goals in total and fell behind after just 25 seconds, they played some sumptuous attacking football in between.
Matheus Pereira sparkled in his first league start behind the striker, and set up goals for Matt Phillips and Jake Livermore, who both impressed.
Grady Diangana also scored an outrageous solo goal, finishing with a cute and audacious chip over goalkeeper Christian Walton after winning possession himself.
After struggling to find the net from open play in their first five games, the Baggies looked incisive in the final third, an threatened regularly.
But there were mistakes at the back from both Kyle Bartley and Sam Johnstone that gifted Tony Mowbray's side two goals.
Following five goals in the first half, there were none in the second, even though Blackburn asked plenty of questions, hitting post and bar and having a goal disallowed.
Bilic made three changes to his attacking forces, and his decision to give Matheus Pereira is first league start in place of Filip Krovinovic proved inspired.
The Brazilian was at the heart of everything good for the Baggies, and played the sort of incisive forward passes the team had been missing.
Charlie Austin and Grady Diangana were also picked ahead of Kenneth Zohore and Kyle Edwards.
But the Baggies got off to the worst possible start, conceding a calamitous goal just 25 seconds in.
In a mistake that mirrored last season's woes at the back, Kyle Bartley played a poor pass in field to Romaine Sawyers, who was tackled on the edge of his own box before Bradley Dack sweeped the ball home.
For the fifth time in their six league games, Albion had conceded first.
Incredibly though, neither side heeded that goal as a warning, with both putting themselves in trouble by continuing to play the ball out from the back.
Diangana started well, and had one shot blocked before calling Christian Walton into action 16 minutes in with a shot from range.
But Pereira looked a cut above anything else on the pitch, and it was the Brazilian who set up Albion's leveller 22 minutes in.
Sawyers atoned for his earlier error by wriggling clear of danger and playing an early pass forward to Pereira, who immediately looked for Phillips' run.
Greg Cunningham tried to hold him off, but Phillips was too fast and too strong for him, and he eventually got round the defender before sliding the ball under Walton.
Blackburn appealed for a foul but referee Tony Harrington was unmoved, and second goal of the season and came a day after his new three-year contract.
Nine minutes later and the Baggies had completed the turnaround.
Darnell Furlong was wreaking havoc up the right hand side, and set up a chance for Pereira, whose header went just wide, before having a hand in the second goal.
The right-back got to the byline again and this time laid the ball back to Phillips, whose audacious chip to the back post from a narrow angle beat Walton but hit the crossbar.
It didn't matter though, because Pereira, with his back to goal, laid the ball off to Livermore, who thundered in his first goal of the season.
The Baggies were purring, and the loanee from Sporting was at the heart of everything.
But then five minutes before the break Diangana got in on the act and made it 3-1 with a solo goal of supreme quality.
After robbing Darragh Lenihan of posession in his own half, the winger left him for dead and burst into the box at speed.
Just when it looked like he should square it to Phillips, he chipped the ball over Walton with such nonchalant panache that it was almost cruel to the Blackburn keeper.
Rovers were their own worst enemy, and playing themselves into trouble at th eback but the Baggies were brilliant, and scored three goals in 18 minutes to take a firm grip of the game.
But then the half ended as badly as it started, with Albion conceding another poor goal.
When Sam Johnstone spilled a header in the box, the Baggies failed to clear their lines and Bradley Johnson eventually poked home from close range to give Mowbray's men some hope.
It was another goal conceded from a set piece, and for all their attacking verve, the Baggies only went into the break one goal ahead.
Mowbray was unhappy though, and he made a double substitution at half-time to try and stem the blue and white tide.
It seemed to work. Blackburn started the second half brightly, passing the ball around neatly before drawing Albion into conceding free-kicks.
The visitors were crowding out Pereira after giving him too much space in the first half and Bilic's men couldn't get out of their half.
Ten minutes after the restart, Rovers had the ball in the back of the net when Dack and Lenihan bundled it in, but the goal was ruled out for a foul on Johnstone.
But the Baggies had a glorious chance to extend their lead when the ball fell kindly to Austin at the back post.
The striker took a touch to set himself, allowing Rovers to fling their bodies in the way and block it.
And that was to be his final piece of action because he was then brought off for Kenneth Zohore.
But Blackburn were still on top, and 65 minutes in they nearly equalised when Dack pulled a free-kick back to Stewart Downing, whose first-time shot hit the outside of the post.
Pereira almost capped off his performance and an impressive team move with a goal, but his curled shot went inches over the bar.
Bilic sent Krovinovic on for Diangana with 15 minutes left in order to give his side more control.
The Croatian flashed a shot across the box and Semi Ajayi forced Walton into a save from a header, but Albion's best chance to score a fourth came in the 89th minute when a free-kick fell kindly to Kyle Bartley at the back post.
The centre-back was five yards out, but he somehow blazed his shot over.
Fortunately, that miss didn't cost the Baggies who enter the international break unbeaten ui in the league with 12 points from their opening six games.
An encouraging start.
01 GOAL BLACKBURN - Dack capitalises on a mistake at the back 25 seconds in
22 GOAL ALBION - Phillips outmuscles Cunningham before sliding the ball under WAlton
30 GOAL ALBION - Livermore cracks one into the far corner after Phillips hits the bar.
40 GOAL ALBION - Diangana scores a superb solo goal
45 GOAL BLACKBURN - Johnson sweeps home after Johnstone spills a header.
45 Mowbray makes a double substitute at half-time
56 GOAL DISALLOWED - Dack and Lenihan bundle the ball into the net but it's ruled out for a foul on Johnstone.
65 POST! Downing hits the outside of the post after a well-worked free-kick.
MAN OF THE MATCH
Matheus Pereira - Sparkled behind the striker in his first league start for the club.
POSITION IN THE TABLE
4th, with 12 points from six games.
Albion (4-2-3-1): Johnstone; Furlong, Ajayi, Bartley, Ferguson; Sawyers, Livermore (c); Phillips, Pereira (Edwards 89), Diangana (Krovinovic 76); Austin (Zohore 68).
Unused subs: Bond, O'Shea, Brunt, Robson-Kanu.
Blackburn (4-2-3-1): Walton; Bennett, Williams, Lenihan, Cunningham; Travis, Johnson (Buckley 45); Downing, Dack, Armstrong (Graham 78); Gallagher (Rothwell 45).
Unused subs: Leutwiler, Nyambe, Evans, Rankin-Costello.
Referee: Tony Harrington
Attendance: 23,792 (1,333 away)