Jonathan Forte put Latics ahead in the opening minutes of the game before Michael Bostwick equalised ten minutes later.
Marcus Maddison gave Posh the lead in the second half but Kusunga's first goal of the season rescued a point and Latics remain eight games unbeaten in all competitions.
Latics made a perfect start going ahead in the opening six minutes of the game. Carl Winchester turned his defender skilfully before feeding a beautifully weighted through ball into the path of Danny Philliskirk.
The forward slipped the ball across the greasy surface to Forte and he made no mistake from six yards out to give the visitors the lead on six minutes.
Posh started to come back into the game and were unlucky not to equalise ten minutes later but Marcus Maddison's shot struck the post.
The home side did however find an equaliser two minutes later through Bostwick. The ball was only half cleared to the edge of the area and the midfielder was there to hammer home from 20 yards to level the scores.
Posh started to dictate proceedings but Latics looked threatening on the counter attack. Winchester, who had been impressive all half, fizzed a ball into the box but unfortunately could not pick out an Athletic attacker.
The visitors almost re-took the lead ten minutes from the break but Posh goalkeeper Ben Alnwick somehow pulled off a save with his leg to deny Forte a second.
Minutes before the break, Peterborough striker Conor Washington found a way past Latics' defence, placed the ball beyond Paul Rachubka but James Wilson was back on the line to clear the danger.
As the pressure looked to have passed, Marcus Maddison thrashed a shot goal wards but Rachubka was down well to tip the ball away.
Latics could have regained their lead on 49 minutes but Forte could not make a clean connection with the ball after Conor Wilkinson's initial shot was deflected into his path.
The visitors would rue that missed chance two minutes later as Posh took the lead. Liam Kelly bundled Maddison to the floor and the midfielder picked himself up and smashed his free kick from 30 yards past Rachubka to give the home side the lead.
Just after the hour mark, Michael Smith thrashed a shot that Rachubka did well to tip away and Posh defender Jack Baldwin was denied on the line as Latics defended resolutely.
There patience paid off a minute later as Latics drew level. Mike Jones' inch-perfect corner found the head of the onrushing Kusunga who scored his first goal of the season to level the game again.
The visitors found an extra gear from the goal and went in search of a winner but were faced with a tough Posh defence.
Maddison, who was an impressive performer for the home side, struck the post from 25 yards, ten minutes from time as both sides went in search of a winner.
Latics raced up the other end and forced their own chance but substitute Dominic Poleon fired wide after great work from Jones.
As we entered the final seconds of the game, Latics won a late free kick. Jones' delivery was half cleared towards James Dayton but the winger fired his shot over the bar and the referee blew time on a pulsating encounter.
Peterborough United: Alnwick, Smith, Baldwin, Bostwick, Payne, James (McEvoy 87'), Washington (Otzumer 81'), Anderson, Newell (Ferdinand 78'), Burgess, Maddison.
Subs not used: Grant, McCann, Santos, Zakuani.
Oldham Athletic: Rachubka, B.Wilson, J.Wilson, Kusunga, Brown, Jones, Kelly, Winchester (Poleon 59'), Forte (Dayton 85'), Philliskirk, Wilkinson.
Subs not used: Coleman, Dieng, Tidser, Turner, Morgan-Smith.
Goals: Peterborough United (Bostwick 18', Maddison 51') 2-2 Oldham Athletic (Forte 6', Kusunga 66')
Attendance: 5,508 (361 visiting supporters)