Schmeichel headed a Danny Drinkwater cross against the underside of the bar and the ball appeared to bounce down just over the line in the first minute of stoppage time – before Chris Wood made sure.
Wood was credited with the goal – but Schmeichel is likely to join his father Peter in the goalscoring goalkeepers’ club courtesy of the dubious goals panel.
It denied relegation strugglers Yeovil victory over the leaders after they had been given a 22nd-minute lead with a free-kick from Joe Ralls.
The late goal stretched City’s unbeaten league run to 18 games – a club record in the second tier of English football.
Both sides were unchanged after weekend draws, with Leicester looking to extend their unbeaten run in the league to 18 matches.
Foxes manager Nigel Pearson took his usual place in the stands after spending two nights in hospital following an illness scare on Saturday. He was given the all-clear after tests.
The Leicester boss must have been as stunned as the fans to see Jamie Vardy miss a sitter in the second minute as the Foxes made a flying start.
The 16-goal striker was put clear by Matty James and with no offside given, was left with only goalkeeper Marek Stech to beat. But Vardy put a tame shot straight at the goalkeeper.
It was a real let-off for Yeovil and despite plenty of possession City lacked the cutting edge they have been showing in recent weeks.
Riyad Mahrez fired straight at Stech after breaking well from midfield and David Nugent saw his close range shot in the 15th minute deflect off Foxes defender Marcin Wasilewski into the arms of Stech as another opportunity went begging.
Leicester paid the price for these missed chances in the 22nd minute as Yeovil took a shock lead.
Danny Drinkwater was penalised for a foul just outside the penalty area and Ralls swerved a lovely free-kick into the far corner beyond the diving Schmeichel.
To their credit, Yeovil were playing a pressing game and giving City little time on the ball.
A corner from the right presented the Foxes with their next chance but Wes Morgan’s downward header bounced up and over the bar.
Mahrez twice blazed shots over the bar from Jeff Schlupp crosses and a disappointing half by Leicester ended with a Drinkwater shot flying just wide of the target.
The second half almost began disastrously for City with Schmeichel having to make a point-blank save to keep out an Ishmael Miller shot from inside the six-yard box.
Miller was proving a real handful for the Leicester defenders and again went close in the 55th minute with his shot this time scraping the far post.
City squandered yet another chance five minutes later when Anthony Knockaert found Schlupp to the left of goal but the full-back drilled his shot wide of the far post.
When Morgan headed wide from a right wing corner and it was starting to look one of those nights for the leaders.
Pearson rang the changes with three substitutions in the space of four minutes sending on Lloyd Dyer, Kevin Phillips and Chris Wood for Vardy, Wasilewski and Nugent.
James almost snatched an equaliser with a surprise shot from 30 yards that Stech just managed to keep out.
But City piled on the pressure in the last few minutes and snatched a point in dramatic circumstances in stoppage time.