David Bell with a fine individual effort, Paul Furlong with his first goal for Luton and Matthew Spring from the spot all found the net after the woeful Gills had somehow been allowed to level in the first half through Mark Bentley.
But Town should have bagged more after a dominant opening 45 minutes which showed a vast improvement from the disjointed display at the County Ground seven days earlier.
In glorious sunshine, Luton began well with Darren Currie in particular using the ball superbly with some accurate cross-field passes.
The goal Luton's enterprising play deserved duly arrived in the 17th minute and in spectacular fashion from Bell.
Picking the ball up wide on the left from Furlong's lay-off, the winger beat Barry Cogan and then cut inside Nicky Southall before unleashing a thunderous low drive that flew in off the foot of the post from 22 yards.
The Hatters should have made it 2-0 three minutes later when Talbot flicked on for Edwards to play in Furlong, but with just the goalkeeper to beat the veteran frontman could only fire into the legs of his former QPR team-mate Simon Royce.
The miss looked as though it could prove costly as Gillingham levelled - and scored their first goal of the season - in the 22nd minute completely out of the blue.
Delroy Facey earned a corner off Richard Jackson with a marauding run and Bentley was left alone to nod in Southall's flag-kick at the near post for a cheap equaliser.
Luton rallied again though and went back ahead as Currie's shot was deflected into the path of Drew Talbot, who crossed from the right-hand side of the penalty area past the badly positioned Royce for Furlong to net with a diving header.
If the first half had been eventful, the second period was the complete opposite as both sets of players appeared to drop into autopilot in the heat.
Town resumed their control and after Southall deflected Bell's goalbound shot wide in the 78th minute, the Hatters sealed the game with Spring's penalty two minutes later.
Substitute Paul McVeigh was sent crashing in the area by Bentley as he ran on to Jackson's chipped pass and Spring found the top corner of the net from the spot despite Royce getting a hand to the ball.