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Gillingham had a first half lead wiped out as Peterborough burst into life after the break.
John Akinde put Gillingham ahead from the penalty spot but Peterborough came out fired up for the second half to lead with goals from Jonson Clarke-Harris (2) and Siriki Dembele.
Visitors Peterborough had the joint worst goalscoring record away from home in League 1 ahead of the match at Priestfield. Despite that they had second place in their sights pre-match.
Gillingham hadn’t managed a win against Posh in the last four meetings at ME7 but were buoyed by a weekend win at Charlton.
The visitors certainly didn’t look like a title-chasing side in the opening half as the Gills dominated, heading into the break a goal up thanks to Akinde’s 31st minute penalty.
There may have been some debate about the penalty decision but the Gills certainly deserved their lead.
Prior to the spot-kick the Gills had kept the visitors pinned in their own half for large periods. Connor Ogilvie fired over and Tommy O’Connor was denied a shot in the box thanks to good defending.
Rare forays forward by the visitors saw a Mo Eisa shot blocked by Ogilvie and a cross/shot from the same player curl narrowly wide.
Ogilvie fancied his chances of scoring from distance after his stunner at the weekend and put another shot over shortly before the opener.
Akinde made the most of the push in the box from Jack Taylor. The Gills striker calmly slotted home the penalty to beat Christy Pym from the spot.
Ogilvie rolled another shot past the post before the interval.
Posh switched formation for the second half, after starting with wing-backs, and introduced lively forward Dembele. They looked a different team.
It was a mistake from Jack Bonham that handed the visitors a leveller, however, spilling a shot from Nathan Thompson into the path of Clarke-Harris and he converted.
The goalscorer went close again moments later with a deflected shot over the bar but it wasn’t long before Peterborough were ahead.
Dembele burst into the box for a 52nd minute goal, his shot taking a deflection to beat Bonham. The Posh forward started and finished the move, running onto a Sammie Szmodics pass and evading a challenge from Dempsey to make it 2-1.
Clarke-Harris put another shot wide as the visitors continued to threaten.
They went 3-1 up in the 68th minute when Joe Ward’s cross was met by Clarke-Harris, flicking it in past Bonham.
Posh defender Mark Beevers got in the way of a header from Akinde with three minutes left to deny the Gills with a chance to get back into the match.
Gillingham: Bonham, Jackson, Ogilvie, Tucker, Cundy, O’Connor (Johnson 64mins), Slattery (McKenzie 74mins), Dempsey, Lee (MacDonald 64mins), Oliver (Graham 53mins), Akinde. Subs not used: Bastien, O’Keefe, Morton.
Peterborough: Pym, Butcher, Johnson, Beevers, Kent, Taylor, Brown, Szmodics, Ward, Eisa (Dembele), Clarke-Harris. Subs not used: Gyollai, Burrows, Blake-Tracy, Kanu, Hamilton, Mason.
Referee: Charles Breakspear