The chance of the match fell to their most experienced striker, Jamie Cureton, in the 78th minute.
The former QPR man was perfectly positioned at the far post to meet a cross from substitute Ricky Shakes. He could have tapped the ball in, but instead blasted it against the bar from three yards.
The result left the Robins in the bottom four while Yeovil, in 18th place, have their heads slightly above the dangerline.
But they are struggling badly with an unprecedented crop of injuries and less than half of the current team could have counted on a starting place earlier in the campaign.
The Yeovil injury jink struck again in the 27th minute when inspirational skipper Terry Skiverton was helped off with a hip injury.
Prior to that the Glovers looked the better side and they could have taken the lead in the 12th minute. Midfielder Paul Terry moved up to meet a cross from Arron Davies, but the ball bounced to safety off a post.
Davies, a former Southampton trainee, was Yeovil's best player and he looked to have broken the deadlock on the hour when he steered home a Kevin Gall cross only to find an assistant's flag up for a marginal offside decision.
Cureton was the liveliest of the Swindon attackers but on this occasion his finishing let him down.
In addition to that late three-yard miss he also wasted their best opportunity of the first half. After giving his marker Scott Guyett the slip, he fired across the face of the goal and wide.
For Swindon, the point was some relief after three successive defeats, including a 7-1 hiding at Nottingham Forest. But both these teams need at least three victories to have a hope of staying up. And both will have to play better than this.