Until Batt cut inside to send a stunning 25-yard half-volley sailing over goalkeeper Brad Jones on 76 minutes it looked as if Gordon Strachan, still seeking a first win four games after replacing Gareth Southgate, would be the manager celebrating after goals from Dave Kitson twice put Boro ahead.
Posh began well, powering forward beneath a barrage of long throws from new capture Exodus Geohaghon who became an instant hit with the London Road faithful.
The 24-year-old, who followed Cooper from Kettering, hurled the ball into the Boro goalmouth with Lee Frecklington and Scott Griffiths both firing narrowly wide before George Boyd saw a 20-yard shot snatched to safety
by Jones.
As Boro became more adventurous, Julio Arca released Leroy Lita for a shot that Joe Lewis blocked with his legs and the Posh keeper also stuck out a boot to deflect an Arca shot on 28 minutes.
This time the ball flew to on-loan striker Kitson and the Stoke man claimed his first Boro goal from the edge of the area.
Posh drew level on 54 minutes thanks to Boyd's 11th goal of the season, a low drive that gave Jones no chance after Scott Griffiths had clipped the ball forward.
Boro edged ahead again four minutes later, Adam Johnson beating full-back Gaby Zakuani before producing a superb cross that Kitson forced in with his head for the 100th goal of his career.
With Cooper urging his men forward from the touchline, Posh again responded with Batt sending the ball into the far corner of the net after Boyd had nodded on a Ryan Bennett pass.