In a game blighted by torrid weather, the Hatters had the best of things with Tom Craddock going the closest to breaking the deadlock shortly before half-time when he hit a post.
The result moved the Bedfordshire side's points tally on to double figures but left them still adrift at the bottom while the Gills kept their promotion hopes alive.
The visitors threatened within 15 seconds as Nicky Southall whipped in a cross from the right, which Mark McCammon just failed to get his head on.
Sam Parkin then went close for Luton in the second minute when he ran in behind the visiting defence only to lift his 10-yard shot past the far post.
Strike partner Tom Craddock then let fly with a 25-yard effort that was pushed aside by Simon Royce four minutes later.
The Gills registered their first attempt on target in the ninth minute when Southall's low 20-yard drive was safely gathered by Dean Brill.
The game then drifted through a lull as both sides struggled to cope with the wet and windy conditions until Craddock's 12-yard shot was held by Royce in the 32nd minute and Chris Martin fired wide from a tight angle for the hosts two minutes later.
Luton came within a whisker of taking the lead two minutes before the break when Sol Davis fed Craddock, who produced a mesmerising turn to leave Mark Bentley standing before curling an 18-yard effort against the foot of the post.
On the stroke of half-time Royce produced a super block to deny Ian Henderson from seven yards after the winger had been played in by the lively Craddock.
The conditions deteriorated after the break and the first glimpse of an opening didn't arrive until the 67th minute when Bentley misjudged a header and Parkin fed Craddock only for Barry Fuller to produce a saving tackle.
Craddock then ended a mazy run three minutes later with a wild left foot shot that flew high and wide from 15 yards.
Craddock then missed Luton's best chance of the half in the 89th minute when he blazed over from 12 yards after Royce had flapped at substitute Jake Howells' corner.