Town took the lead in the first half through a Joe Ralls free kick and were cruelly denied the three points thanks to the Leicester City shot stopper.
The Glovers were lucky not to have been a goal down after just two minutes whrn Jamie Vardy beat the offside trap to race through on goal. But somehow the striker tamely shot straight at Stech in the Town goal.
Town soaked up the early pressure from the home side and took the lead after 22 minutes. Good control and quick footwork by Tom Lawrence saw him get upended about 25 yards from goal.
Lawrence picked himself up to stand over the ball with Edwards and Ralls. It was Ralls who stepped up to curl the ball around the wall and into the corner of the net past the full stretched Schmeichel.
At the other end Leicester has a great opportunity to level the scores but Mahrez shot high over the bar from close range.
Just as the first half was coming to a close Miller dragged a shot narrowly wide of the upright and at the other end Drinkwater found himself in space but his shot also went wide of the target.
After just two minutes of the second half Yeovil could have doubled their lead. Good determination on the right by Dawson saw him manage to keep the ball in play and cross to Miller. The on loan striker controlled the ball and turned in the area only to see his goal bound shot well saved by Schmeichel.
Ten minutes into the second period and with the game stretched, Edwards intercepted a pass in the centre circle. The midfielder surged forward and played a neat pass to Miller. The big striker cut inside onto his left foot and fired a shot towards goal, only for the ball to go narrowly wide.
Stech had been relatively quiet in the first 80 minutes but had to be on his toes to dive well to his left to deny a long-range James effort.
With two minutes left of the 90 Leicester were throwing everything at the Yeovil defence. Shane Duffy was on hand to block a certain goal when the ball fell to one of the man Leicester players in the area.
With three minutes signaled by the fourth official the home side sent Schmeichel up for a corner, he got his head on a cross that smashed against the bar, with the home fans appealing for a goal the Chris Wood prodded home to make sure the goal counted.