Both are 8-under par and lead world No. 2 Rory McIlroy by one shot heading to the weekend at PGA National.
Rose shot a second consecutive 4-under 66, while Gillis tied the course record of 64 in his second round, along with Graeme McDowell.
McIlroy, who shot 67 on Friday, can supplant Luke Donald for the top spot in the Official World Golf Ranking with a win.
Tiger Woods shot 68 on Friday to get to the weekend on 1 under and trails the leaders by seven shots.