The Gills did most of the damage in the first half, going 3-0 up thanks to a Danny Kedwell penalty in the fifth minute, a header from the same player 10 minutes later and Charlie Lee's nodded effort seconds before the interval.
Chris Whelpdale headed in a fourth eight minutes from time for the hosts, who now have 16 points from their opening six league fixtures this term.
At the start of the day they had been a point clear of second-placed Exeter, who drop to fourth after their 1-1 home draw with York, a result they salvaged through John O'Flynn's late equaliser after Michael Coulson had put the Minstermen in front.
The Grecians have been leapfrogged in the table by Port Vale and Fleetwood, who both join them on 13 points after victories.
Vale are up to second with a 3-1 win at Plymouth, who were ahead through Robbie Williams before the away side responded with a Jennison Myrie-Williams penalty and goals from Ashley Vincent and Ben Williamson.
Third-placed Fleetwood, meanwhile, secured their three points right at the death as Andy Mangan's stoppage-time header earned them a 1-0 triumph at home against Northampton, the visitors having been reduced to 10 men in the first half by Danny East's dismissal.
Accrington stay fifth after a 1-1 draw at Dagenham, Peter Murphy ensuring Stanley's point late on by cancelling out Luke Howell's goal for the hosts.
Alex Revell's finish saw Rotherham to a 1-0 home victory over Torquay which saw them move up to sixth, while Bradford advanced into the final play-off berth with a 3-0 home win against rock-bottom Barnet, second-half goals from James Hanson, Alan Connell and Andrew Davies sealing it.
Southend came from behind to beat Cheltenham 3-1 away, the visitors hitting back after Jermaine McGlashan's early goal through Sean Clohessy, Britt Assombalonga and Mark Phillips.
Calvin Zola and Jacques Maghoma notched a brace each as Burton routed Oxford 4-0 at home, while Aldershot and Morecambe drew 0-0.
Elsewhere, Rochdale defeated Wimbledon 2-1 away, Dele Adebola and Bobby Grant putting the visitors in charge in the first half - with visiting striker Jack Midson being shown a red card between the two goals - before Luke Moore's late reply, and Chesterfield won 3-1 at home against Wycombe.
Wanderers had Leon Johnson sent off after only 10 minutes and the hosts soon took advantage, Chris Atkinson and Jack Lester swiftly netting. A Neal Trotman own-goal gave Wycombe hope, but Sam Hird then added Chesterfield's third.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!