Batt fired an unstoppable right-foot volley deep into injury time, just nine minutes after Simon Cox thought his 16th of the season had given Swindon a first win in five.
Peterborough had earlier levelled via an own goal from Robins midfielder Jon-Paul McGovern, who just ten minutes prior to that misdemeanour had set up full-back Jack Smith for the opener.
On a bitterly cold night Peterborough suffered an early blow as defender Gaby Zakuani was forced off inside the first ten minutes after he collided awkwardly with the advertising boards.
The home side took advantage of the indecision in the Posh defence by snatching the opening goal with McGovern's intelligent cross picking out the on-rushing Smith, who stabbed his volley past Joe Lewis for his second of the season.
Early evidence suggested though Peterborough were by far the better footballing side and before too long they had crafted an equaliser. George Boyd broke down the left and sent a teasing low cross into a crowded penalty area which McGovern clumsily attempted to clear, only to put it into his own net.
Boyd was a growing influence on the game but despite Posh enjoying large areas of possession they could not break down a resolute Town defence.
The second half began in a similar fashion to the way the first one ended with Posh continuing their dominance of the ball, but unable to find a way past Phil Smith.
Swindon then perhaps sensed the game was theirs for the taking as they forced Lewis into two saves.
First McGovern tested the England Under-21 International with a free-kick, before another set-piece found its way to the Scottish midfielder waiting on the edge of the penalty area, but his well-struck volley was gathered cleanly.
Aaron McLean, six minutes later, raced clear of the Swindon defence to round Phil Smith, but the angle proved too tight and as he tried to tee up Craig Mackail-Smith and the Swindon goalkeeper recovered to block the ball off for a corner.
The Robins must have thought they had won it when Michael Pook's 20-yard strike cannoned off the face of Craig Morgan and into the path of Cox, who despite appearing offside, gratefully accepted the fortune.
But as the clock ticked down Batt's brilliance secured a point for the Posh.