Two goals from Swindon's leading scorer Sam Parkin looked to have put the home side on their way to victory to boost their hopes of a play-off place before Clarke struck with the final kick of the game.
The defender escaped marker Grant Smith to latch onto goalkeeper Brad Jones' long clearance downfield and fire home a low shot into the far corner from a tight angle.
Blackpool striker Keigan Parker gave the visitors the lead after 18 minutes when he beat Swindon's offside trap and buried a shot in the bottom right-hand corner, for his eighth goal of the season.
But Parkin turned the game in favour of the home side with two goals in the final nine minutes of the first half.
There was a slice of good fortune in his first as Sammy Igoe blocked a clearance and the ball ricocheted into the striker's path for him to shoot home from ten yards.
Parkin then produced a finish of real quality in first-half injury-time for his second as he chested down Smith's pass before calmly lifting a shot over Blackpool goalkeeper Jones.
The former Chelsea frontman wasted two good chances to complete his hat-trick after the interval but Blackpool deserved their late equaliser as they peppered Rhys Evans' goal in the second half.
Evans reacted smartly to produce a double save in the 49th minute, blocking efforts from Parker and his strike partner Simon Lynch, while he did even better four minutes later to again deny Lynch.
Blackpool sent on new Serbian striker Zarko Grabovac for the final 12 minutes as they searched for an equaliser and his presence helped cause confusion in Swindon's penalty area, helping Clarke to score his fourth goal of the campaign.