Forster ran onto a flick-on from Glenn Murray to fire past man-of-the-match Steve Collis.
Earlier the Crewe keeper kept his side in the game with a string of fine stops from Forster and Adam Virgo.
Debutant Calvin Zola got his home career off to a good start with the 85th minute equaliser, but justice was done when veteran Forster struck.
Dean Cox and Kevin McLeod provided some excellent delivery for rampant Albion as Crewe flayed around in unconvincing fashion at the back
It was Virgo who had secured his side a 36th minute lead on his return to the club from Celtic.
He rose unchallenged on the far side of the box to loop a header past Collis after McLeod fired the ball in.
Yet Crewe should have been in front by then but Zola headed a Billy Jones free-kick wide with the goal at his mercy.
Forster's powerful 12th minute run past Julien Baudet almost set up the opener with Steve Thomson and Virgo messing up chances to finish from close range.
Crewe created little after Zola's early chance, although Shaun Miller flicked a low cross from Jones over and the lively Joel Grant forced Michel Kuipers into a save at his near post.
Murray had the ball in the net in the 22nd minute, but climbed all over Collis as he rose high at the back stick to head home.
Forster came close to extending the lead when he crashed a shot across the face of goal five minutes before the break.
After the break, Murray came close to finishing off McLeod's cross and centre-half Colin Hawkins headed onto the foot of the post.
Teenager James Bailey came to Crewe's rescue when he cleared Murray's near-post header off the line.
Crewe introduced summer signing Anthony Elding in place of Miller on 67, but it was another substitute Ben Rix, who set up Zola for the equaliser.
The Congolese striker beat the offside trap and finished coolly across Kuipers.