Both shot 6-under 66 at Bay Hill to take a two-shot lead over Nick Watney.
Dufner has now opened his last three PGA Tour starts with 66.
Kim holed out for an ace at the par-3 17th en route to the early lead before fading on his second nine.
Ernie Els, who must finish runner-up or better to get into the Masters, is 1 under and T-17.
Phil Mickelson struggled off the tee through his first round, shooting 73.