The 36-year-old's first top-flight strike since October 23 cancelled out a first-half opener from Luis Sinisterra in a fiery Yorkshire contest, but a point has done little for either side's hopes of avoiding the drop to the Championship.
Aiming to take advantage of Leeds' recent spate of shambolic defensive performances, Leicester enjoyed the better of the opening exchanges and thought that they had broken the deadlock in the seventh minute as Youri Tielemans rolled back the years.
Doing his best to replicate his stunning winner in the 2021 FA Cup final, Tielemans unleashed a thunderous first-time effort into the top corner via the crossbar after Leeds failed to close him down, but VAR came to the Whites' rescue.
The ball had found its way to Tielemans from a corner, where Harvey Barnes initially flicked the ball goalwards towards Boubakary Soumare before the ex-Lille man prodded it back towards the Belgian, but he was in an offside position from the set-piece and the goal was chalked off.
Leicester continued to come forward in droves and were agonisingly close to breaking the deadlock in the 17th minute as Kelechi Iheanacho lifted a cross towards the back post, but James Maddison could only poke his effort wide on the stretch - much to the amusement of the Elland Road faithful.
Having weathered the Leicester storm, Leeds began to attack down the Foxes' left-hand side and experienced plenty of joy in doing so, opening the scoring with 20 minutes gone as Sinisterra rose highest to nod home Jack Harrison's cross to the back stick.
There was not too much in the way of a response from the visitors, but Leeds soon lost goalscorer Sinisterra to an injury sustained in a challenge from Caglar Soyuncu. Once again, Wilfried Gnonto was overlooked as Crysencio Summerville came on in the 32nd minute.
Nevertheless, with the returning Maddison and Barnes leaving a lot to be desired in the final third, Leeds got to half time with their slender lead intact, and their efforts to frustrate Leicester early in the second half worked to a tee.
Dean Smith's side huffed and puffed but struggled to create inroads, as Barnes fired over the top with 57 minutes gone before Maddison struck the wall with a free kick in a brilliant position.
Illan Meslier - who has been the subject of incessant criticism recently - was left with very little to do as the Leeds defence held firm, but he produced a brilliant double save to keep out Iheanacho and Patson Daka in the 73rd minute, although the latter was offside on the follow-up anyway.
However, after two of Leicester's strikers were thwarted, it was third time lucky for the Foxes, as Iheanacho and Maddison combined on a lightning-quick counter attack, and the latter played through Vardy to curl home into the bottom corner with 10 minutes remaining to level the scores.
In the process of charging at the Leeds backline, Iheanacho appeared to tweak his groin just before playing the pre-assist to Maddison - the Nigeria striker fist-pumped in the direction of the away end as he trudged off to be replaced by Dennis Praet.
Only three minutes after a customary wind-up celebration, Vardy had the ball in the back of the net again as he slotted home from Daka's ball across, but the flag immediately went up for offside - the 36-year-old wagged his finger to the linesman in disapproval, but replays showed that he had indeed gone too early.
The Foxes' tails were up, but it was the hosts who passed up two gilt-edged opportunities from corners approaching the 90-minute mark, as Daniel Iversen made a terrific point-blank save from Marc Roca's header before Patrick Bamford produced one of the misses of the season - fluffing his lines from a yard out at the back post.
A stalemate keeps 16th-placed Leeds one point and one place better off than Leicester in 17th, but Everton are within touching distance of the two teams and could leapfrog both of them with a win over Newcastle United on Thursday.
Leeds now prepare to travel to Bournemouth in another crucial relegation scrap on Sunday, before Leicester attempt to steer clear of Everton in Monday's basement battle with the Toffees.