Gary McSheffrey scored twice as Coventry dented 10-man Gillingham's survival hopes at Priestfield.
Michael Doyle's 25-yard free-kick made it 1-0 before Andy Morrell and McSheffrey combined for two more.
Gillingham improved after the break and Gary Wales and Mamady Sidibe cut the deficit, although player-boss Andy Hessenthaler was sent off in between.
But McSheffrey latched on to a Stephen Warnock through-ball and Richard Shaw smashed home to seal the rout.
The Gills were ripped apart in a superb opening spell from the visitors, which began with Doyle curling home effort after Alan Pouton had brought down McSheffrey.
It was no surprise when McSheffrey played in Morrell and the latter planted the ball past Steve Banks.
From the next attack McSheffrey picked up a pass from Morrell and jinked inside the last defender before curling a delightful effort into the net from 20 yards.
Scott Shearer was forced into his first save in the 33rd minute when he turned away Hessenthaler's header from Nicky Southall's flighted free-kick.
Banks then made a smart stop to block McSheffrey's shot from the edge of the box as Coventry continued to open up Gillingham with ease.
The Gills had much more of a cutting edge after the break and Cox and Southall both went close before Wales linked up well with Sidibe before firing home.
Gillingham dealt a blow moments later when Hessenthaler was dismissed for a second bookable offence but they made it 3-2 when a long throw was flicked on by Patrick Agyemang and Sidibe smashed the ball past Shearer.
Any hopes of a comeback were extinguished when McSheffrey grabbed his second, and Shaw piled on the misery in stoppage time.
Gillingham: Banks, Cox, Hope, Leon Johnson, Southall, Hessenthaler, Pouton, Spiller, Hills, Agyemang, Sidibe. Subs: Ashby, Brown, Saunders, Jarvis, Wales.
Coventry: Shearer, Deloumeaux, Konjic, Davenport, Warnock, Safri, Barrett, Doyle, Gudjonsson, Morrell, McSheffrey. Subs: Brush, Jorgensen, Kerr, Shaw, Whing.
Referee: A Bates (Staffordshire).