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Darren Byfield and Neil Harris struck in either half to record the Gills' first away win of the campaign.
Andy Robinson did mange to pull one back from the penalty spot after Mike Flynn was sent off for the visitors but it was too little, too late.
And it keeps Swansea's awful run of results going to put the pressure on manager Kenny Jackett.
Jackett had made five changes from the side that went down to local rivals Bristol City, notably in attack where hamstring victim Lee Trundle was replaced by recent signing Leon Knight.
The ex-Brighton hitman partnered fellow new boy Rory Fallon in the Swans frontline, the target man making his home bow following his £300,000 switch from Swindon.
And the pair came close to making the perfect start after four minutes, Knight crossing after neat work down the right and Fallon glancing a header wide.
But despite the promising opening, the hosts were behind on 18 minutes when Flynn was allowed to advance and set up Byfield to shot home from the edge of the area.
Swansea's frustrations grew as Gillingham's resolute defending only allowed the hosts a few harmless pot shots at goal before the half-time whistle.
Jackett's cause was not helped when Darren Way failed to emerge from the tunnel after the interval thanks to injury, Adrian Forbes replacing him in midfield.
The Swans found little respite from a physical and determined Gillingham, but tempers boiled over on 68 minutes when Flynn picked up two yellow cards in the space of 60 seconds to receive his marching orders.
But just two minutes later Harris had wrapped up the win for the visitors when a quick counter attack caught Swansea cold and the former Cardiff striker tapped home from close range.
Swansea fought back when Knight was pushed by Leon Johnson on 83 minutes, Robinson pulled a goal back from the spot.