Darren Ferguson's side clinch victory in Kent.
Jonson Clarke-Harris scored a brace as Peterborough came from behind to beat Gillingham 3-1 at the MEMS Priestfield Stadium.
The Posh striker scored the first and third goals as the visitors scored three in the second half, ensuring all three points.
John Akinde had given Gills the lead in the 32nd minute. The striker won a penalty after being shoved in the back when climbing for a header. He stepped up himself to slot the ball into the centre of the goal, whilst Christy Pym dived to his left.
Peterborough came out all guns blazing in the second half and two goals in four minutes turned the game on its head.
Nathan Thompson dribbled to the edge of the Gills penalty area before shooting. Bonham was unable to keep hold of the shot, and the rebound fell to Clarke-Harris who bundled the ball into an empty net.
Siriki Dembele grabbed the second as his smart dink over Bonham put Peterborough in front.
Clarke-Harris got his second, and the visitors third, in the 67th minute.
He met a Joe Ward cross with a back-heel, which left Bonham rooted to the spot and the effort bounced into the bottom corner.
Steve Evans made one change to the starting 11 that beat Charlton. Callum Slattery was fit enough to start the game having missed Saturday’s win, and replaced Stuart O’Keefe as he continued to build his match fitness.
Jordan Graham returned to the squad but was only fit enough to start on the bench.
There was a shout for a penalty in the fifth minute after Robbie Cundy went down inside the penalty area. The referee however wasn't moved.
Connor Ogilvie had the first chance of the game in the 11th minute. Tom O’Connor’s corner was flicked towards the goal but ricocheted in the direction of John Akinde. He played a smart lay off to Ogilvie, but his right-footed effort went just over the crossbar.
O’Connor had a golden chance in the 15th minute. A high Ryan Jackson cross was knocked down by Vadaine Oliver. It fell to O’Connor who looked set to score. However, a vital block took the velocity off the effort.
Ogilvie tried his luck from distance with the hope of replicating his goal from last Saturday. However, he curled his shot wide of the target.
In the 30th minute, the Gills were awarded a penalty.
A ball into the box was aimed for Akinde, but as he leapt for the header, he got pushed in the back. He crashed to the floor, giving the referee no choice but to point to the spot.
Akinde took the penalty himself and slotted it into the centre of the net as Christy Pym dived to his left.
Oliver was brilliantly denied a scoring opportunity moments before the break. He managed to get around Mark Beevers, but as he went to shoot, Beevers did brilliantly to block. However, Oliver booted the bottom of his foot, and it caused him some discomfort.
Ogilvie came inches away from making it two on the stroke of half-time.
Akinde latched onto a loose ball and laid it off to the defender, but his fizzed effort across goal went inches wide of Pym’s post.
HALF-TIME: Gillingham 1-0 Peterborough United
Peterborough brought on Siriki Dembele at the interval and his arrival, along with a change of shape, seemed to give Peterborough a lift, and they netted three times in 32 minutes.
Firstly, a low effort from the edge of the box could only be parried by Jack Bonham, and Clarke-Harris was well placed to slide in to find an empty net.
Soon after, it was 1-2. Dembele had half a yard inside the box for a shot; it took a wicked deflection which took the effort beyond the reach of Bonham and into the net.
The introduction of Jordan Graham offered Gills a threat on the right hand side, and a series of crosses kept the Posh defence alert, but as the hosts tried to pull level, Darren Ferguson's men added a third.
Ward, operating at right-back, found space for a cross and Clarke-Harris provided a clever back flick to find the net and give Gills a mountain to climb.
Gills sent the ball forward in their attempts to set up a grandstand finish; Akinde and Cundy both had half chances but Peterborough stood firm to secure victory.
FULL-TIME: Gillingham 1-3 Peterborough United
Gillingham: Bonham, Jackson, Tucker, Cundy, Ogilvie, Slattery, O'Connor (Johnson 65’), Dempsey, Lee (MacDonald 65’), Akinde, Oliver (Graham 53’)
Unused Substitutes: Bastien, McKenzie, Morton, O'Keefe
Peterborough United: Pym, Butler, Thompson, Beevers, Kent, Brown, Taylor, Ward, Szmodics, Clarke-Harris, Eisa (Dembele 46’)
Unused Substitutes: Gyollai, Burrows, Blake-Tracy, Kanu, Hamilton, Mason
Referee: Charles Breakspear