While Korean Charlie Wi and American Jason Dufner share a two-shot lead after each shooting six-under-par 66s on the opening day at Bay Hill, and Nick Watney lies alone in third after a 68, three-under 69s from Woods and Rose have put them solidly in the frame in a seven-way tie for fourth.
The vaunted duo are tied with the likes KJ Choi, Anthony Kim, Bubba Watson, Sean O'Hair and Jimmy Walker.
in his first tournament since returning from injury after injuring his Achilles two weeks ago, is a six-time winner of this event, and gave himself a solid enough start from which to potentially launch a seventh title assault.
Woods made only one bogey from a three-putt at the short 17th and otherwise looked in control, not showing any signs of lingering injury concerns as he rolled in four birdies.
"For some reason the course just fits my eye," he said.