With previous leaders Leyton Orient not in action until Tuesday, Mark Warburton's men accepted the opportunity to take over at the summit.
Brentford's unbeaten run in the league now stands at 16 matches and they have still to lose under Warburton, who succeeded Uwe Rosler in December.
Former Gillingham loanee Jonathan Douglas scored the only goal of first half in the 22nd minute, the experienced midfielder arriving unchallenged in the box to convert a cross and punish the club he briefly represented in 2005.
A penalty from Marcelo Trotta made it 2-0 with 20 minutes remaining after Tony Craig had been hauled down in the box.
Cody McDonald took just three minutes to pull a goal back for Gillingham, but the strike proved no more than a consolation.
Brentford are now two points clear of Orient, while Gillingham remain 14th.
