Swansea had lost their last three games against the Gills but goals from Bayo Akinfenwa and Andy Robinson made sure the jinx was broken.
Akinfenwa opened the scoring in the sixth minute when he nodded home a Lee Trundle cross before substitute Robinson put paid to a Gillingham comeback when he drove home on 72 minutes.
Swans boss Kenny Jackett opted to keep new signing Pawel Abbott on the bench having splashed out £150,000 on the Huddersfield Town striker just 24 hours earlier.
But he was almost immediately rewarded when Trundle helped to open the scoring. Having gone close just moments earlier, Trundle's cross was headed home by Akinfenwa who glanced the ball past Roman Larrieu and into the net.
Larrieu, who was making his debut after arriving at Priestfield on loan from Plymouth Argyle, was soon called into the action again as Swansea dominated the early stages.
Tom Butler saw the keeper palm away his shot after the midfielder had jinked his way into a goalscoring position.
He was soon called into the action again, this time keeping out a Tom Williams effort. However, Gillingham went close to pinching a leveller when Mark Bentley almost headed home a Sean Clohessy cross only for Willy Gueret to clear the effort off the line.
Gillingham rallied after the break and could have snatched an equaliser when Garry Mulligan got free to head goalwards only for his effort to come back off the woodwork.
But Swansea then wrapped things up when Robinson came off the bench in the 66th minute and, six minutes later, he drove home past Larrieu after working a neat one-two with Akinfenwa.
Abbott did come on to make his debut with five minutes remaining but Swansea had already won the contest as they revived their promotion hopes.