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Gills were knocked off top spot after a day to forget at Coventry.
Home forward Jacob Murphy hit a first half hat-trick as the Gills conceded four goals in a torrid 10-minute spell.
It was all-but over for the League 1 leaders before the break.
Bradley Dack reduced the deficit with half an hour left but the Gills were unable to inflict any further damage.
Justin Edinburgh’s side had gone into the top of the table clash at Coventry buoyed by a 3-1 victory over Bury the week before.
An enforced change at the back saw Deji Oshilaja replace Harry Lennon, after being recalled by Charlton the day before, while former Coventry striker Cody McDonald was picked to partner Dominic Samuel in attack.
There was only one team in it during the first half as the hosts attacked down both flanks. They out-classed the Gills.
Gillingham’s best chance led to them conceding the opener. Bradley Dack’s corner was headed at goal by McDonald but when Jim O’Brien cleared off the line the hosts broke in numbers.
Oshilaja made a mess of his back-pass and Murphy capitalised, running in on goal and converting from an angle with 34 minutes gone.
Three minutes later it was 2-0 as Ryan Kent's corner was headed home by Ben Turner.
Coventry were rampant and they had a third with 41 minutes gone. O’Brien picked out a run from Murphy, slicing Gills’ defence in two, and he converted.
Murphy completed his 10-minute hat-trick with Coventry’s fourth as he tucked away a left-sided cross.
Doug Loft replaced Osadebe at the break and an early chance for Samuel was deflected wide for the Gills.
The Gills pulled a goal back in the 63 minute when Jackson’s low cross found Dack and he found the bottom corner.
Samuel tried his luck from the edge of the box, as the Gills got more of the ball after the goal, but the shot was comfortably saved by Reice Charles-Cook.
Coventry: Charles-Cook, Ricketts, Stokes, Martin, Turner (Phillips 55mins), Vincelot, Fleck, Kent, O’Brien (Haynes 81mins), Murphy (Bigirimana 64mins), Armstrong. Subs not used: Burge, Lameiras, Tudgay, Antoine-Fortune.
Gillingham: Nelson, Jackson, Garmston, Egan, Oshilaja, Wright (A Morris 70mins), Hessenthaler, Osadebe (Loft 46mins), Dack, McDonald (Dickenson 68mins), Samuel. Subs not used: G Morris, Ehmer, McGlashan, Donnelly.
Attendance: 15,604 (857 away)