Darren Ferguson's men made it three wins from three in all competitions with a 4-2 win at Notts County.
Peterborough United made it three wins from three in all competitions and took their goal tally to 10 for the week after another emphatic display on the road with a 4-2 rout of Notts County at Meadow Lane.
In an open start to the game, Posh could have found themselves in front inside five minutes as Tommy Rowe fed Daniel Kearns, but his low shot was saved by the legs of Bialkowski.
Posh appealed for a spot-kick moments later as Assombalonga tumbled under the challenge of Leacock, but the referee gave the decision in the home side's favour.
Assombalonga saw a clever flick saved by Bialkowski on six minutes after a good move involving Kearns and Tomlin.
However, it was the home side who found the breakthrough, as a cross from the left was powerfully headed past goalkeeper Olejnik by centre back LEACOCK who had stayed up from the previous set-piece.
The lead didn't last long as within three minutes a corner from Lee Tomlin was headed home at the near post by Tommy ROWE.
Barnett headed a chipped cross from Assombalonga wide of the target on the half hour mark after the former Watford man had squirmed his way into the box.
Olejnik made a smart stop to deny McGregor on 39 minutes after an error from Rowe on the edge of his own defensive box. McGregor fired wide of the near post moments later as the first half entered the final five minutes.
On 53 minutes, after a relatively scrappy start to the second period, Posh got their noses in front as Rowe fed BARNETT who coolly slotted the ball past the goalkeeper for his second goal of the campaign.
On 58 minutes, Posh made it 3-1 as Tomlin was upended in the box and calmness personified, Grant McCANN stepped up and dinked the ball down the middle giving the goalkeeper no chance.
Olejnik beat away a fierce free-kick from Labadie on 62 minutes before the home side appealed in vain for a penalty kick as Ntlhe appeared to handle inside the area.
Kearns fired over after a mistake from Bialkowski as Posh went in search of a fourth goal.
On 70 minutes, it was 4-1 as a terrible back header from Leacock was capitalised on by Britt ASSOMBOLANGA, he took a touch and rifled an unstoppable shot past Bialkowski for his second goal of the season.
Kearns limped out of proceedings to be replaced by Daniel Swanson 10 minutes from time. Barnett headed a Swanson cross over the top before teenager Jaanai Gordon was introduced into the fray.
Deep into stoppage time, substitute ARQUIN coolly converted from the spot after Zakuani was penalised for handball inside the box.
Final Score: Notts County 2-4 Posh
Notts County: Bialkowski, Dumbuya, Sheehan, Leacock (c), Tempest, McGregor, Labadie, Campbell-Ryce (sub Thompson 84min), Fotheringham, Haynes, Showunmi (sub Arquin 68min). Unused subs: Spiess, Thompson, Boucaud, Haworth, Zoko, Coombes.
Posh: Olejnik, Alcock, Bostwick, Zakuani, Ntlhe, McCann, Rowe, Tomlin, Kearns (sub Swanson 79min), Barnett, Assombalonga. Unused subs: Day, Sinclair, Knight-Percival, Gordon, Payne, Little.
Attendance: 6,582 (2,102 Posh fans)