Andrew Shinnie gave the visitors the lead when he expertly fired in from the edge of the box after a well-worked one-two with Harry Cornick midway through the first half, before Elliot Lee converted from James Collins' cross ten minutes after the restart.
Cornick nearly netted an outrageous goal after he went on a 70-yard run, going past two Gillingham players before seeing his low effort hit the post, but Lee was there to follow up for his eighth goal of the campaign and the Town's third on the afternoon.
Gillingham's top scorer Tom Eaves got a goal back with 20 minutes to play, but a late bombardment from Steve Lovell's side was well weathered by the Hatters.
Jones said: "I'm delighted with the three points, any three points is a good three points.
"I thought it's not the best, most picturesque game, most fluent game, because of how they play, they restart everything and go into Eaves, so it's a real disjointed game. But the game should have been over by half-time.
"We scored, we had perfectly good goal disallowed and we should have had a penalty on 45 minutes, absolute stonewall, no question about it, not even debatable, it should have been over at half time.
"I don't want to get myself in trouble, but what a great ball in and a great leap, bang, a good goal, old striker's goal. It's really disappointing because it could have been a lot easier afternoon and I'm having to make changes to make sure we see the game out.
"It should have been 3-0 at half time, or 2-0 at half time and a chance on 45 minutes to have a penalty from 12 yards to make it 3-0 and game done."