Tommy Mooney scored twice to continue his spectacular start to his Swindon career but his team threw away a golden chance to win.
With the scores 2-2 Mooney was pushed in the area at a corner by Blackpool goalkeeper Lee Jones to concede a penalty.
But Jones made up for his mistake by diving low to his left to push away Sam Parkin's spot kick.
The unmarked Mooney opened the scoring in the eighth minute when he headed in a centre from the left by David Duke.
But Blackpool were level two minutes later when a long throw by Mike Flynn caused confusion in the Swindon box and Jonathan Douglas scored with a 15-yard left-foot shot.
Mooney, a bargain summer signing from Birmingham City, clipped the top of the Blackpool bar after 25 minutes before Blackpool went ahead.
Mike Sheron got away down the left and his cross found Scott Taylor who beat goalkeeper Rhys Evans with a low left-foot shot in the 26th minute for his sixth goal of the season.
But Swindon were not to be denied and a minute later they got their equaliser when big defender Matt Heywood crossed from the right and Mooney back-headed a spectacular equaliser.
Sheron almost put Blackpool ahead in the 56th minute when a long kick out by Jones left Andy Gurney and Evans dithering and Sheron prodded wide from a good position.
Jones continued his second-half defiance of Swindon with a decisive block from Mooney's powerful 20-yard free-kick but both teams had to settle for a hard-earned draw.
There was disappointment for Swindon in the 78th minute when midfield player Steve Robinson was carried off on a stretcher after appearing to hurt his left ankle.
Referee Steve Tomlin booked Parkin and Duke of Swindon for fouls and Blackpool trio Douglas, also for a foul, and Danny Coid and Taylor for dissent in a competitive second half.