The deadlock was broken on 10 minutes as a corner from Grant McCann was met by Swindon defender Branco who powered a header past his own goalkeeper from 10-yards.
It was 2-0 on 14 minutes as a scrappy piece of defending and a bit of persistence from Assombalonga saw the ball fall to Kyle VASSELL and the former Bishop Stortford man found the bottom corner with his left-foot for his first goal in Peterborough colours.
Danny Swanson clipped the top of the crossbar with a free-kick on 20 minutes after Rowe was upended 25-yards from goal.
Nathan Thompson was lucky to escape just a caution for a late lunge on Swanson on 24 minutes. Vassell fired over with his left-foot moments later after good determination and persistence from both Rowe and McCann.
A strong run from Ben Gladwin was ruined by a poor finish at the other end following a mazy dribble as Swindon came close to reducing the arrears.
McCann escaped a sliced clearance from a corner kick with Olejnik just about grabbing the ball before it crossed the line. Vassell then saw a low shot saved by the legs of goalkeeper Foderingham.
On 31 minutes, Swindon pulled a goal back as Nile RANGER escaped the offside trap and calmly rolled the ball past the advancing Olejnik.
Swindon were reduced to 10-men on 33 minutes as Assombalonga was caught with a high boot by McEveley who was shown a straight red card by referee Mr Tierney.
Assombalonga was forced off the field following that challenge with Danny Kearns introduced from the bench as his replacement. On the stroke of half-time, Rowe was cautioned for charging into his opponent.
Moments later, Swindon were level and it was the second own goal of the contest as a low cross was sliced by Shaun Brisley and via the inside of the post found its way into the back of the net.
Darren Ferguson made a change at the interval with Jermaine Anderson replacing Grant McCann. Defender Ward came close to putting the visitors in front with a powerful looping header, aided by the wind, on 54 minutes, but thankfully for Posh it drifted wide.
Payne saw a powerful drive blocked superbly as Posh pushed to get themselves back in front. Gladwin fired over for the Robins just past the hour after the ball ran kindly to him 25-yards from goal.
Kasim fired wide on 66 minutes as the game became stretched in difficult conditions. Foderingham did well under pressure from Vassell to prevent the ball from creeping over the line as the high wind played a part with Swanson's header hanging in the air.
Joe Newell replaced Brisley as Posh made a change in formation for the final quarter of proceedings. Knight-Percival headed over from a Kearns corner kick on 79 minutes.
Final Score: Posh 2-2 Swindon Town
Posh: Olejnik, Alcock, Brisley (sub Newell 77min), Bostwick, Swanson, Payne, Assombalonga (sub Kearns 42min), McCann (sub Anderson 46min), Vassell, Rowe, Knight-Percival. Unused subs: Day, Little.
Swindon: Foderingham, Thompson, Luongo, Ranger, N'Guessan, McEveley, Kasim, L. Thompson, Ward, Branco, Gladwin (sub Byrne 88min). Unused subs: Belford, Reis, Harley, Barker.
Attendance: 3,312 (304 Swindon fans)