Blackburn, who had to play for 55 minutes a man down after their opening goalscorer Benni McCarthy was sent off, were facing defeat following second-half goals from Roman Bednar and Ishmael Miller.
But Andrews, a £1.3million capture from MK Dons in September, popped up in the last minute to rescue a share of the spoils.
It was rough on Albion who had fought back from McCarthy's early goal with a storming second-half display.
Even after Andrews struck, they still had a chance to win the game, but Bednar saw his header saved by Paul Robinson.
The draw did at least end Albion's run of three straight defeats but this was two points thrown away.
Blackburn are now five games without a win but Paul Ince can take heart from his side's commitment to chase a seemingly lost cause.
Albion got off to the worst possible start when Ryan Donk, who conceded the penalty that put them on the way to defeat at Newcastle United on Tuesday, landed them in trouble again by gifting Blackburn a spot-kick.
There appeared little danger when Jason Roberts collected the ball with his back to goal on the right-hand side of the area.
But for some inexplicable reason Donk grabbed his shirt and referee Michael Jones had no hesitation in awarding a penalty.
McCarthy made no mistake with his spot-kick which he blasted past Scott Carson - little knowing this his match would shortly be over.
Albion's players were visibly angered by the penalty and immediately went in search of an equaliser.
But James Morrison's drive was beaten away by Paul Robinson, Borja Valero chipped over the bar and Gianni Zuiverloon failed to get his header on target from Paul Robinson's cross.
Albion's hopes were then raised when McCarthy needlessly saw red. McCarthy, who had been booked in the 19th minute for a foul on Jonathan Greening, was dismissed after 35 minutes when he handled a clearance from team-mate Martin Olsson while tussling with Donk.
While that should have given Albion an edge, Blackburn were unfortunate not to increase their lead before half-time.
Brett Emerton's injury-time strike from 18 yards was goalbound, before being tipped around the post by Carson.
It was a decisive moment as fired-up Albion launched a furious assault at the start of the second half and were rewarded in the 55th minute after 60 seconds of penalty area chaos.
Miller hit the post with a low drive and in attempting to make his clearance, Blackburn skipper Ryan Nelsen crashed the ball against the post and crossbar.
Robinson then beat away Robert Koren's drive but Blackburn's luck ran out when Valero fed Miller and his short pass was converted by Bednar from 12 yards.
Blackburn were being completely overrun at this stage and Miller's wonder strike completed the Albion comeback.
Picked out by Greening with his back to goal, Miller turned neatly before beating Robinson with a powerful drive in the 62nd minute.
It was a goal worthy of winning any game, but never-say-die Blackburn were not to be denied and when Roberts won the ball he fed Andrews, who beat Carson with a low 20-yard drive.