Club-record signing Assombalonga enjoyed a competitive debut to remember for Peterborough as he struck the winner against Swindon on the opening day of the Sky Bet League 1 season.
The 20-year-old striker, a summer capture from Watford, scored the only goal of the game with a fierce right-footed winner early on.
The victory sees Posh claim a very early advantage over promotion favourites Wolves, who played out a goalless draw with Preston in their first match.
Coventry's problems continued as, after fighting back from two goals to draw level at 2-2, they conceded a late goal to lose 3-2 at Crawley.
The Sky Blues, who start the new campaign with a 10-point deduction, had looked to have salvaged a point when second-half goals from Callum Wilson and Franck Moussa saw them cancel out early efforts from Jamie Proctor and Joe Walsh
However, the visitors were left empty-handed when Mike Jones netted an 84th-minute winner for Crawley.
Bristol City, who came down from the Championship alongside Wolves and Peterborough, drew 2-2 at home to promoted Bradford at Ashton Gate.
Scott Wagstaff and Jay Emmanuel-Thomas twice put the hosts ahead but goals from Nahki Wells and Rory McArdle earned Bradford a point.
None of the four sides who were playing League 2 football last season managed to start with a win as champions Gillingham were beaten 1-0 at home by Colchester, substitute Andy Bond netting the winner late on, while Rotherham and Port Vale both drew.
Rotherham did well even to get a point though after trailing 3-1 at Crewe with five minutes to, goals from Ben Pringle and Lee Frecklington salvaging a 3-3 draw for the visitors.
Crewe were 2-0 up in the first nine minutes through Anthony Grant and Max Clayton, and Harry Davis made it 3-1 after Frecklington had pulled a goal back.
Vale drew 1-1 at home with last year's losing League 1 play-off finalists Brentford, who went ahead through Shaleum Logan's fine first-half solo goal only to be pegged back by Doug Loft's equaliser moments later.
Leyton Orient took advantage of Lee Miller's first-half dismissal to run riot in a 5-1 win at Carlisle.
Orient took the lead through Kevin Lisbie's stooping header and after Miller was sent off for clattering Nathan Clarke, who was taken to hospital, Scott Cuthbert headed home the visitors second.
Carlisle pulled one back through David Amoo's penalty, but David Mooney's header and two curling efforts from Dean Cox sealed a superb win.
There were also plenty of goals at Stevenage where visiting Oldham claimed a 4-3 win with Jose Baxter striking with a late penalty to clinch his side the points.
Darius Charles put Stevenage ahead before goals from James Tarkowski, Baxter and Christian Montano made it 3-1 to Oldham.
The home side hit back through Greg Tansey and Filipe Morais, but Baxter slotted the winner four minutes from time.
Craig Westcarr struck twice and also set up Chelsea loanee Milan Lalkovic for another goal as Walsall earned a 3-1 home win over Tranmere, who replied through Andy Robinson's free-kick.
In the other game, Shrewsbury and MK Dons shared a goalless draw.