The striker ran from the halfway line before burying a drive into the corner to close the gap to safety to just three points.
It clinched back-to-back Barclays Premier League wins for the Foxes for the first time since September but they remain bottom with seven games left.
Robert Huth's late header had made it 2-2 after Darren Fletcher and Craig Gardner scored for Albion, while David Nugent levelled in the first half before the Foxes' late show.
The Baggies, playing in a special replica kit from the 1968 FA Cup final as they paid tribute to former striker Jeff Astle to help launch a foundation in the late striker's name, are seven points above the bottom three.
Craig Dawson returned from suspension for Chris Baird while Claudio Yacob replaced the benched Stephane Sessegnon.
Marc Albrighton was recalled for Leicester, in place of Riyad Mahrez who dropped to the bench at The Hawthorns.
The Baggies began well and Joleon Lescott had already headed a corner over before another brought the hosts' opener after eight minutes.
Brunt's delivery was met by Fletcher seven yards out and his glancing effort flashed past Kasper Schmeichel, with goal-line technology awarding the goal after Esteban Cambiasso failed to clear in time.
But the midfielder played his part in the Foxes' leveller on 20 minutes when his deep free-kick was nodded down by Leonardo Ulloa for Nugent to steal in and prod under Boaz Myhill from seven yards.
The striker scuffed wide from 18 yards four minutes later but the Baggies regained the lead on 26 minutes through Gardner's second goal of the season.
Chris Brunt's deep cross found Brown Ideye and the striker managed to nod the ball back for Gardner to hook in to the corner, via a deflection off Wes Morgan.
The Foxes felt the ball had gone out before Brunt crossed but their protests went ignored.
But three minutes before the break the Foxes should have levelled when Ulloa - without a goal in his last nine games - missed a fine chance.
Albrighton's cross was flicked on by Nugent for Ulloa and, under pressure, he blazed over from six yards.
The Baggies had been second best since taking the lead and they continued to struggle to create after the break.
Saido Berahino failed to pick out Gardner in space during a brief dangerous spell but there was little to concern the Foxes.
Leicester looked the more dangerous but, as so often this season, struggled to turn their efforts into chances and goals.
Mahrez fired a free-kick over with 18 minutes left with their first serious chance of the second half
But they kept pressing and levelled with 10 minutes remaining.
Nugent hooked a deep ball back into the box with the Foxes queuing up at the far post and Marcin Wasilewski's header found Huth to nod in, with Dawson helping the ball into the net.
And Vardy clinched a priceless win in injury time when he outmuscled Gareth McAuley on the halfway line, arrowed towards goal and buried an unstoppable low finish past Myhill from 12 yards.
Source : PA
Source: PA