Swansea City's five-game unbeaten run in League One came to an end at Priestfield Stadium as Leon Knight's late strike was their only consolation.
It was a double from Trinidad & Tobago international defender Ian Cox and a third from Matthew Jarvis which earned the Gills a deserved victory.
Gillingham: Flinders, Jupp, Cox, Johnson, Jackman, Bentley, Flynn, Crofts, Jarvis, Easton, Mulligan (Ndumbu-Nsungu 60). Subs Not Used: Pouton, Spiller, McDonald, Clohessy.
Swansea City: Gueret, Amankwaah, Iriekpen, Lawrence, Austin (Williams 55), Britton (Butler 55), Tate, Pratley (Way 55), Robinson, Knight, Akinfenwa. Subs Not Used: Fallon, Oakes.
Att: 5,500
Swans boss Kenny Jackett made just one change to the side that won 2-0 at Brentford with Andy Robinson coming in for Tom Butler who had to be content with a place on the bench.
With Lee Trundle injured (knee), Knight continued up front alongside Adebayo Akinfenwa with Rory Fallon on the bench.
Gillingham, full of confidence after two straight wins, started brightly and took the lead in the 14 minute.
Good work by Matty Jarvis won the Gills a corner which Easton played short to Jackman on the left. His cross fell for Ian Cox who slotted a shot past Willy Gueret.
Robinson blazed over the bar from distance in the 28th minute, but the Swans found themselves further behind two minutes later.
Michael Flynn and Matty Jarvis combined well before Jarvis beat Dennis Lawrence for pace to fire into the top corner.
The Swans nearly reduced the deficit after the interval when Lawrence met a Robinson free-kick only to direct his header just wide, while Akinfenwa fired against the post from a Butler cross.
But Gillingham put the result beyond doubt in the 79th minutes when the Swans failed to deal with a corner from Easton and Matty Jarvis found Cox to make it 3-0.
With five minutes left of normal time Swansea did manage a consolation effort when Knight followed up a save from Scott Flinders to make it 3-1.
The defeat saw the Swans slip down to eighth.
