After a first half of few opportunities, Scott Wharton's goal three minutes into the second looked to be enough to give Rovers all three points at Ewood Park.
But as chances came and went for the home side, Albion struck in added-time at the end of the game as Samir Nabi converted from the spot after Ryan Nyambe was adjudged to have handled.
However there was still time for a further goal with Wharton heading home a carbon-copy of his first to ensure a fourth consecutive victory for Rovers.
At a chilly Ewood it was Damien Johnson's side who started the brighter of the two with Lewis Hardcastle seeing an early effort deflect narrowly wide.
The resulting corner saw Rovers threaten once more but Connor Thomson mis-kicked in front of goal as the chance went begging.
Further opportunities were few and far between as neither side impressed. The visitors had a couple of sights of goal through forward Tyler Roberts, but Simon Eastwood in the Rovers goal saved comfortably.
Rovers ended the half with a decent shout for a penalty after Joe Rankin-Costello looked to have been hauled down in the area, but the officials were unmoved.
Whilst the first half was low on entertainment, the start to the second couldn't have been more different.
Rankin-Costello thought his goal-bound shot in the 49th minute was blocked by a West Brom arm, but they were only awarded a corner kick.
However Rovers took full advantage of the situation as Connor Mahoney delivered to the back post and captain Wharton rose highest to power his header home.
It was a lively start to the second half for Johnson's young side, showing much more urgency and tenacity in their play, and they should have scored further goals.
The impressive Rankin-Costello saw an effort kept out by Alex Palmer in the West Brom goal, but the keeper was helpless as Rovers almost doubled their advantage on the hour when Matty Platt was unfortunate to see his header crash down off the crossbar and away.
Hardcastle was then next to try his luck, Palmer scrambling the ball clear as Rankin-Costello closed in.
Albion pressed for a way back with a pair of dangerous crosses, before Jonathan Leko, who featured as a substitute against Manchester City in the Premier League on Saturday, put a shot just beyond the far post with Eastwood at full stretch.
But just as it looked like Rovers had seen the game out to claim another win and a clean sheet, the visitors were awarded a soft penalty kick.
As the home side struggled to clear their lines in their own area, the ball was adjudged to have struck the arm of Nyambe and referee Ricky Wootton pointed to the spot.
Baggies captain Samir Nabi took responsibility from 12-yards and made no mistake to make it 1-1 in the second minute of four added on at the end of the match.
However the young Rovers are made of stern stuff and immediately went back on the attack with Anton Forrester winning a corner kick.
Mahoney delivered from the left once more, and just like the opening goal in the 49th minute, Wharton rose impressively to plant his header into the back of the net to win the game.
The young Rovers centre-half had tasted the disappointment of defeat in the semi-finals of the FA Youth Cup on Friday night. His double tonight went some way to erasing that heartache.
The result means Rovers need just a point from their final league game next Monday night against Aston Villa to secure a top-five finish and a place in the end of season play-offs.
ROVERS: Eastwood, Nyambe, Doyle, Tomlinson, Platt, Wharton (c), Mahoney, Rankin-Costello, Forrester, Hardcastle (sub Mansell 90+2 mins), Thomson (sub Wall 79 mins).
Subs not used: Travis, Fisher (GK), Carson.
Goals: Wharton 49, 90+3 mins.
WEST BROM: Palmer, Fitzwater (sub Wilson 77 mins), McCourt, Field, Donnellan, Jones, Scrivens (sub Edwards 62 mins), S Nabi, Roberts (sub Smith 82 mins). Ward, Leko.
Subs not used: Sweeney, Ross (GK).
Goals: Nabi (pen) 90+2 mins.