The Gills raced into a two-goal lead through Jack Payne's 20-yarder and Danny Kedwell's header after 11 minutes.
Jack Saville nodded Barnet back into the game but Deon Burton restored the two-goal cushion six minutes before half-time.
Exeter made it three wins from three away games as they ended Oxford's 100% home record with a 4-2 victory at Kassam Stadium.
Jamie Cureton's well-taken finish from distance, Scot Bennett's header from Liam Sercombe's corner and another from veteran striker Cureton put the visitors three clear.
Jake Forster-Caskey's penalty and Alfie Potter's header reduced the arrears, but John O'Flynn settled matters before James Constable received two quickfire bookings late on.
Port Vale's Tom Pope hit four goals against former club Rotherham in a 6-2 rout.
Louis Dodds and Ashley Vincent grabbed their other goals, while Michael O'Connor and Daniel Nardiello (penalty) netted for the shellshocked Millers.
Jon Parkin's hat-trick swept Fleetwood to a 4-0 win at Morecambe - their third successive league victory.
The summer signing grabbed his first goals for Town but was grateful to Andy Mangan for all three assists as the burly striker bagged two close-range finishes and a header.
Parkin then turned provider as he crossed for Barry Nicholson to nod home late on.
Jason Walker maintained York's unbeaten run as he snatched a late equaliser in a 2-2 draw with Chesterfield.
Walker struck in the final minute to make it four unbeaten for the hosts, who had twice fallen behind to Sam Hird and Craig Westcarr.
Michael Coulson scored their initial equaliser.
Northampton condemned AFC Wimbledon to a third successive away defeat after goals from Alex Nicholls and Chris Hackett completed a 2-0 win.
Wycombe received the perfect start against Cheltenham but failed to capitalise in a 1-1 draw at Adams Park.
Cheltenham's Keith Lowe scored an own goal after only three minutes but the visitors levelled when Shaun Harrad scored from the spot after Stuart Lewis fouled Marlon Pack.
Torquay claimed their first clean sheet in four games as they fought out a goalless draw with Plymouth.
Substitute Fabian Broghammer saved Bristol Rovers from a fourth defeat in as many home games after scoring from close range to secure a 2-2 draw with Aldershot.
His 90th-minute strike came after David Clarkson's opener had been washed out by Craig Reid and Alex Rodman's strike.
Matthew Paterson scored his first goal for Burton to seal a 1-0 victory at Rochdale, while Accrington and Bradford drew 1-1, with Padraig Amand and Alan Connell trading goals.
Britt Assombalonga scored twice as Southend beat Dagenham - who had Luke Wilkinson sent off with eight minutes gone - 3-1.
Dwight Gayle scored for the Daggers, with Ryan Cresswell adding a third for Southend.
