Assombalonga broke the deadlock with his 30th goal of the season, firing past Gills goalkeeper Stuart Nelson at his near post following a 41st-minute knockdown from recalled full-back Kgosi Ntlhe.
Only a five save from Bobby Olejnik preserved Posh's advantage as he kept out a classy chip from Cody McDonald in the first attack after the break, but the hosts then dominated the second period.
Skipper Tommy Rowe doubled their lead in the 58th minute with a rasping 20-yard drive that crashed in off the underside of the bar and Assombalonga should have added another six minutes later.
Posh's record signing earned a penalty when brought down by Bradley Dack but saw his tame effort from the spot saved by Nelson.
Assombalonga was later denied by a fine Nelson save and a goal-line clearance from Adam Barrett, but two goals proved enough for Posh to build a six-point cushion over the chasing pack.