At four under par, the Englishman was two shots clear of America's Jason Dufner in the battle between this year's major winners.
At one stage Rose, USPGA champion Dufner and Masters winner Adam Scott were all tied on four under, but the latter two fell away over the closing holes.
Dufner bogeyed the 14th and the 16th at Port Royal to drop to two under while Australian Scott made a double bogey at the 16th to drop three off the lead.
Rose had also dropped a shot at the 14th but he birdied the 17th to pull away from his rivals.
Open champion Phil Mickelson is not in Bermuda and his place has been taken by Padraig Harrington, who replaced Ernie Els last year and won the tournament.
His title defence did not get off to a good start, though, the Irishman carding four bogeys and a double bogey to finish his round three over par.