Kirk, a former resident of the island, shot a two-under 68 after fighting back from being two-over through 12.
The 28-year-old rolled in three consecutive birdies on 13-15 and then drained his clutch putt on the last in his quest for a second PGA Tour win.
Baird gave away two early birdies with back-to-back bogeys at nine and 10 before finishing with a flourish to card a round of 67.
The 41-year-old has made 364 previous starts and earned $12,699,237 (7,927,114 pounds) without a win, the most money of any non-winner. He will have a great chance to break the drought after birdies on the final three holes.
"I'm most looking forward to picking up my first PGA Tour win," Baird said confidently post-round.
"It's that simple. It's not all or nothing. I'm not going to say that, but obviously I have put together some good rounds this week and the thing I am most inspired about this week is outside of the first day, the last two days I don't feel like I played fantastic by any means.
"I scored fantastic and anytime you are tied for the lead after three rounds that's fantastic."
Sitting in a tie for third just a shot behind are Americans Kevin Stadler and Brian Gay along with Australian John Senden.
Stadler, another journeyman with 235 starts on the tour without a win, carved out a five-under 65 in a round featuring seven birdies.
The son of former Masters champion Craig Stadler, he delivered four birdies in a five-hole stretch between the 13th and 17th holes.
"I hit it pretty nice, I didn't make too many mistakes, I hit a lot of fairways and it was a pretty simple round of golf with a lot of fairways and a lot of greens and knocked a couple of putts in," Stadler said
"I'm certainly a lot more comfortable now. It took me quite a while to kind of feel I belonged here and to just settle in. But I've been out here quite a while now and haven't had too many chances to win so certainly looking forward to tomorrow, it should be fun."
Four-time winner Gay's round of 66 featured four birdies in the opening nine holes while Senden poured in a birdie on the 18th to finish with a 68 and a big chance to add to his lone tour win from 2006.
Brendon Todd (67) and Scott Brown (68) share sixth at eight-under while big names Webb Simpson (71) and Matt Kuchar (68) are within striking distance in a group at six-under par.
"It was nice to get a few birdies coming in. It's pretty amazing to do three straight rounds of 68 but looks like I might need to go a lot deeper than that tomorrow to catch these guys," world number eight Kuchar said.
(Reporting by Ben Everill in Los Angeles, editing by Gene Cherry)
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