Stewart equalised with a close-range finish after Chesterfield had dominated a scrappy match but they could not add to Alan O'Hare first goal of the season.
The rousing performance that had knocked West Ham out of the Carling Cup on Tuesday night was unlikely to be repeated but it was still an impressive display from the home side that were unlucky not to go in front in the first half.
Yeovil were well-organised but the passing was poor and Stewart was an isolated figure for much of the opening 45 minutes.
When the Glovers switched to a 4-4-2 formation in the second half, their use of the ball continued to let them down and Chesterfield appeared to be heading for victory until Stewart pounced two minutes from the end.
By then the Spireites should have had the match sewn up but Yeovil's defence, in which skipper Terry Skiverton was outstanding, kept them in the game.
Caleb Folan was always a threat with his pace and power and the legs of keeper Steve Mildenhall rescued Yeovil when the striker whipped in a low shot early in the game.
However, clear-cut chances were few and far between until Yeovil allowed a free-kick from Kevan Hurst to reach O'Hare who made no mistake with a right-foot volley from eight yards in the 50th minute.
The marking was dreadful for that goal and Hurst threatened to take the match away from Yeovil with a stream off crosses from the left but the ball would not fall to a blue shirt.
But Yeovil didn't look like scoring themselves and it was a shock when they did create an opening in the 89th minute.
Substitute Ishmael Welsh crossed to the back post and Chris Cohen headed the ball back for Stewart who guided it over the line with a diving header.