It looked like Saido Berahino's early strike would be all that separated the sides but three goals in eight frantic minutes mean the League One promotion hopefuls will get another chance at the ABAX Stadium next month.
Shaquile Coulthirst equalised after 79 minutes but Berahino quickly restored West Brom's lead before substitute Jon Taylor levelled things up again with four minutes remaining.
West Brom began brightly and created an opening after just 50 seconds
James McClean put a low cross straight into the path of Rickie Lambert but rather than shoot first time he tried to take a touch and ran the ball out of play
Less than a minute later another raid down the left by McClean almost saw him pick out Berahino with a cut back but the pass was behind the incoming striker
Peterborough settled thereafter but following a decent spell of possession they fell behind after 14 minutes
Harry Beautyman gave the ball away in midfield, not for the first time in the early stages, allowing Lambert to lead an Albion break
Lambert held play up well before laying the ball off to striker partner Berahino who beat Ben Alnwick with a 25-yard shot
Peterborough were becoming their own worst enemy and presented West Brom with two more chances either side of the half hour mark
First, Michael Smith sold Alnwick short with a back pass and Lambert caught him in possession however the Posh goalkeeper reacted quickest to grab the loose ball
Then on the other side of the pitch, Ricardo Santos gave the ball away to McClean but Alnwick did well to block his shot when exposed one-on-one with the Republic of Ireland international
After what could be described as comical defending came a genuinely funny moment from Peterborough boss Graham Westley who, in the 55th minute, fell to the floor as if shot when a bang was heard as the match ball burst
Westley muddied his suit but he won a decent laugh from The Hawthorns crowd
Peterborough cut out the silly mistakes after the break and made West Brom work for their chances, which became few and far between
Craig Gardner should have done better than blast his effort over the crossbar from Salomon Rondon's cut back midway through the second half
At the other end Posh were beginning to make inroads and home goalkeeper Boaz Myhill was extended for the first time after 72 minutes when he had to get down to smother Smith's low shot
With 11 minutes remaining, after failing to capitalise on Peterborough's defensive errors in the first half, West Brom were punished for one of their own
A long ball forward caused hesitancy between Sebastien Pocognoli and Myhill and Coulthirst took advantage to score from the right side of the penalty box
Posh were level just five minutes, though
They should have cleared Craig Dawson's cross but the ball found its way to Berahino who finished clinically
However, Posh were not beaten and Taylor found the bottom corner of the net with a shot from the edge of the area
Source : PA
Source: PA