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Rory Donnelly hit an injury-time winner for the Gills at Crewe on Saturday.
The Gills returned to the top of League 1 as the top two teams lost.
Crewe’s Adam King missed a sitter in an opening half that ended goalless.
Cody McDonald hit a post for the Gills in the second half but Donnelly won it at the death.
Gillingham made two changes to their team, with Aaron Morris and Bradley Garmston returning to the starting XI.
Bottom club Crewe were chasing their first home win of the season.
Bradden Inman had the ball in the net for Crewe early on, but referee David Webb rightly ruled it out as he handballed in the build-up.
Gillingham were playing with Luke Norris as the lone striker but he limped off with an ankle injury midway through the half, having landed awkwardly from a challenge.
John Egan had one of Gills’ best chances of the half, side-stepping a player before shooting at goal. Keeper Ben Garratt made the save.
Bradley Dack also came close, with a shot at goal as everyone expected the cross, but it drifted just wide of Garratt’s far post.
Those chances punctuated a half that failed to take off. The Gills allowed Crewe too much space at times and they created some good chances, none better than the one at the end of the half that King somehow failed to convert.
Nelson parried a shot from Inman into the path of King but he shot over from just a few yards out, with the goal open. Pressure from Garmston may have played a part in making the Crewe player miss an easy chance.
McDonald volleyed an effort wide for the Gills early in the second half and with almost an hour gone he hit a post.
Garmston had done well with a run and cross, defender Jon Guthrie couldn’t clear his lines and McDonald had a shot saved from the keeper. His follow-up from an angle bounced out after hitting the far post.
Two minutes later the substitute striker headed a great chance wide after being picked out by Dack.
Dack was the provider again with six minutes left, with a free-kick that Harry Lennon headed just the wrong side of a post.
Referee Webb waved away desperate late penalty shouts from Crewe after a challenge from Egan on Ryan Colclough.
Donnelly made it six goals in four games with a great effort in stoppage-time. He picked up the ball from an angle and curled a fine shot past the keeper into the top corner.
Crewe: Garratt, Turton, Guthrie, Nugent, Atkinson (Haber 73mins), Inman, Dalla Valle (Cooper 40mins), Fox, King, Kingsley (Baillie 80mins), Colclough. Subs not used: Nizic, Jones, Wilson, Ainley.
Gillingham: Nelson, A Morris, Garmston (Dickenson 82mins), Lennon, Egan, Wright (Jackson 64mins), Hessenthaler, McGlashan, Donnelly, Dack, Norris (McDonald 28mins). Subs not used: G Morris, Ehmer, Osadebe, Houghton.
Attendance: 3,924 (310 away)