The 20 year-old hot-shot struck for the third successive league match when arrowing a 25-yard strike past Latics keeper Mark Oxley.
The spectacular 34th-minute strike was all that separated the sides in a wind-ravaged contest until Assombalonga was scythed down by Oxley with eight minutes remaining.
Transfer-seeking Lee Tomlin made no mistake from the spot to ensure Posh pocketed maximum points and celebrated by applauding the home fans.
Tomlin, who had a written transfer request rejected during the week, had fired inches wide moments earlier.
But Oldham refused to roll over and staged a rousing late fightback.
Substitute Charlie MacDonald halved their arrears when nodding in from close range in stoppage time and they came agonisingly close to a leveller in the last action of the game, but defender James Tarkowski failed to make contact with a Korey Smith header with the goal at his mercy.