Among the first onto the course, Haas set the early target with a bogey-free six-under 66 that no one could match, sending the American to the top the leaderboard where he was joined much later in the day by the British world number five.
Rose, who held a two-shot overnight lead, missed a three-foot par putt on 18 that would have given him the outright lead, but his bogey gave him a two-under 70 that put him level with Haas at nine-under 135 for the tournament.
Lurking one shot back is American John Huh (69) while compatriots Ken Duke (68), J.J. Henry (67) and Jimmy Walker (69) are three off the pace on 138.
"The finish kind of got the better of the whole group," said Rose, who was partnered with Woods and South African Ernie Els. "The atmosphere seemed to change when it started to rain.
"I kind of lost my focus. Well, not lost my focus, but just kind of second guessed that putt down the hill a little bit on the speed once the rains fell."
As disappointed as Rose was in his finish it was nothing compared to the frustration Woods felt about the sloppy end to his two-under 70.
A steady rain added to a miserable day for Woods, who had been within striking distance of the leaders until a late round meltdown that started when he found the water with his second shot on the par-five 16th.
There was more trouble off the tee at 17 when he sailed his ball over the green then watched his chip roll well past the cup en route to another bogey.
Left with a 30-foot putt for par at the 18th, the 14-times major winner nearly ended his day on a positive note but was left hanging his head in disbelief when his ball stopped two inches from the hole.
"It's just the way it goes," shrugged Woods. "Sixteen was unfortunate, 17 I made a bad swing and 18 I made a bad swing.
"So all three holes I hit beautiful putts and I thought I made them but they're not realistic putts.
"They're outside that range, so I need to do a better job like I did most of the day getting in the stiff and making those putts."
Despite his collapse, Woods is still well within reach of an eighth Bay Hill win, sitting four off the pace with Fijian Vijay Singh (68) and American Mark Wilson (68).
"I was up, at one point, one back and right there," said Woods, who can reclaim the world number one ranking from Rory McIlroy with a win on Sunday. "The good news is we've got 36 holes to go ... and certainly four shots can be made up."
Bay Hill is routinely used as a final tune-up for the Masters and some past champions will no doubt be concerned about the state of their game before heading to Augusta.
Defending Masters champion Bubba Watson (71) is one-over for the tournament, narrowly avoiding the cut that fell at three-over, but three-times winner Phil Mickelson (79), South African Trevor Immelman (72), Argentine Angel Cabrera (77) will all have the weekend off to think about the year's first major.
"The course set up was just perfect to identify the guys that are playing good and the guys who aren't because, as difficult as this course is, the greens were receptive," said Mickelson after a round that included two triple-bogeys.
"Obviously, I played terrible, and I deserved to shoot a score like this."
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