The striker took aim with his left foot from outside the right corner of the box six minutes after the break and drilled an unstoppable 25-yard shot into the opposite top corner of the net.
And two minutes from time the powerful forward brushed aside his marker, outstripped two defenders and dinked the deftest of shots over City goalkeeper Frank Fielding.
Tyrone Barnett had fired Posh into a 24th-minute lead, shooting home from close range after Fielding could only parry a 20-yard shot from Craig Alcock.
Fielding atoned for his error three minutes later, diving to his left to save Lee Tomlin's penalty following a trip by James O'Connor on Assombalonga.
At that point Peterborough were well on top and much as City huffed and puffed they could make little impression on the visitors.
City boss Sean O'Driscoll is still waiting for his side's first league win following relegation last season.
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