Grant beat three men before finishing brilliantly to earn all three points for a Glovers side who were superb all afternoon and who had deserved victory after a hugely improved showing.
Both sides hit the crossbar in a feisty, often frenetic paced match but none of the near 4,000 crowd could begrudge Gary Johnson his first home win of the campaign.
The manager had reacted to the midweek home draw with basement side Crewe by making three changes to the starting eleven and opting to go for the same side that finished that Alex match. It meant a start for Kieffer Moore up front and Joel Grant moving out wide right to link up with full back Seth Twumasi behind him. Nathan Ralph came in on the left to provide more attacking verve.
And it was Ralph who came close early on when he sliced a shot wide on three minutes after Grant had picked up a poor free kick from Posh keeper Ben Alnwick. Ralph’s corners were also posing problems for the Posh defence and Aaron Martin’s header was blocked from another set piece.
Visiting striker Marcus Maddison was the main threat for the visitors and after scuffing his first attempt on goal, he then hit two long range shots, the first of which went narrowly wide and the second saved by Jake Kean.
The home fans really got behind the new improved Glovers but they had their hearts in their mouths on 27 minutes when Maddison’s curling effort bounced down off the underside of the crossbar and away to safety. Maddison, prone to theatrics at times, made his opinion clearly felt to the assistant referee that he thought the ball had crossed the line but no goal.
Five minutes later, it was Yeovil’s turn to hit the crossbar. Jack Price swung in a dangerous corner and Moore’s flick header was tipped onto the bar by a desperate Alnwick.
Within a seconds, Nathan Smith hit a screamer just wide of the goal as Yeovil looked certain to grab the lead.
Ref Simon Hooper was baffling both dugouts and sets of fans with some peculiar decisions and he started the second half in infuriating style. Moore, played through one on one with the keeper, saw his attempted lob palmed behind for a corner but a goal kick was given. Next, a clear offside decision in Yeovil’s favour saw the ref give a dubious advantage to the Glovers where there was none and Ralph had to pull down Maddison and earn a yellow card to stop a dangerous break.
Joe Edwards hit a rising half volley a yard wide but as you thought the Glovers would have to take a breath and regroup, they continued attacking and always looked the more likely to score. At one stage, it was almost incessant corners from both sides as Yeovil attacked; Martin headed one onto the roof of the net from a Twumasi cross and Ajay
Leitch-Smith forced Alnwick into a smart save with his legs.
Martin then earned a yellow after bringing down Maddison in full flight although the forward’s dramatics after contact made the official’s mind up for him about a card.
Peterborough threatened in patches with Maddison testing Kean and sub Grant McCann offering a different option from set pieces. But just as it looked like it would be the most entertaining 0-0 you’ll see all season, up came a stunning winner.
Ajay Leitch-Smith burst through the middle then played the ball wide right to Joel Grant. Grant cut inside the box, sidestepping two challenges before fooling a third, dummying the keeper and put it into the opposite corner for a superb winner.
In truth, it was no more than the Glovers had merited for their best performance of the season. They played at a high tempo for ninety minutes and created more chances than a side renowned for attacking.