On a day when the club marked the 20th anniversary of the death of icon Jeff Astle, goals from Cedric Kipre, Karlan Grant and Grady Diangana secured a vital win for Valerien Ismael' side.
The scoreline, though, doesn't quite tell the story of the game with the visitors sitting in a low block and showing next to no ambition right from the very first whistle.
Darren Ferguson's side came with a game plan to frustrate and time waste in the hope of pinching a point.
And they almost did it - with Kipre finally opening the scoring in the 78th minute.
From there the floodgates opened with Grant and Diangana going to get the goals Albion's dominance deserved.
And that, overall, was no more than Ismael's side deserved - with the Baggies now just four points behind second-placed Bournemouth following their loss to Hull.
With Albion in desperate need of a win, Ismael handed a first start to £7million striker Daryl Dike when naming his starting line-up.
The American was one of three changes from the defeat at QPR with centre-backs Kyle Bartley (injured) and Cedric Kipre (suspended) both returning after missing the trip to Loftus Road.
Kipre and Bartley joined Matt Clarke in the back three with Darnell Furlong and Conor Townsend at wing-back in Ismael's 3-4-3 formation.
In central midfield, Adam Reach got the nod to partner Jake Livermore.
Up front, Matt Phillips and Grant operated either side of Dike.
Peterborough lined-up in a 5-3-2 formation with Jonson Clarke-Harris and Siriki Dembele their front two.
In a match that was effectively attack versus defence from the first whistle, the visitors immediately sat in a deep back five and challenged Albion to break them down.
And Ismael's men had three decent opportunities to open the scoring inside the opening half-hour - with all three falling for Dike.
The striker almost opened his Baggies account in the 10th minute when he met a cross from Furlong only to see his glancing header sail wide.
He came even closer midway through the half when a long-distance strike from Livermore took a deflection before bouncing kindly for the American in the box.
Dike then looked to side-foot the ball past Steven Benda but his effort was too close to the keeper who made a comfortable stop.
With Peterborough showing absolutely no ambition and content to sit in their low block - Albion - and Dike - continued to press in a bid to find a breakthrough.
And they threatened once again when Kipre sent in a cross which the former Orlando man headed over.
Albion should have been ahead just seconds after the re-start when Kipre sent in a dangerous cross which Dike again glanced wide.
Moments later the striker had to come off after appearing to pick up a slight hamstring issue - with Albion not taking any chances with their new recruit.
Grady Diangana replaced him in a move that saw Phillips become the Baggies central striker.
Albion were now laying siege to the Peterborough goal.
Diangana saw a strike from the edge of the box saved before Grant saw an effort just yards out well blocked by a defender.
The game was now simply a question of whether Albion could score.
And in the 78th minute, they finally did it - with Ismael's side finally getting the touch of luck they deserved.
Following a corner, the ball broke for Furlong who lashed it at goal.
And his effort smashed into Kipre with that deflection taking it over the line.
With five minutes to go Albion doubled their advantage.
Robinson sent a ball over the top with Grant carried into the box before firing past Benda in the visitor's goal.
Albion then added some icing on the cake with a third thanks to a brilliant strike from Diangana.
Again it was Robinson who was the provider with the forward sending a clever ball over the top.
And Diangana produced an outstanding touch to take it into the box before then producing an even better finish to find the far corner.
Albion (3-4-3): Button, Kipre, Bartley, Clarke (Robinson 74), Furlong, Livermore, Reach, Townsend, Phillips (Molumby 75), Dike (Diangana 52), Grant (Fellows 90).
Subs not used: Palmer, Taylor, Gardner-Hickman.
Peterborough (3-5-2): Benda, Edwards (Knight 49), Beevers, Kent, Burrows (Ward 84), Mumba, Taylor, Norburn, Grant (Szmodics 69), Clarke-Harris (Marriott 74), Dembele.
Subs not used: Blackmore, Poku, Tomlinson.