Woods, who was level with compatriot Grayson Murray in the clubhouse, bogeyed the second before three birdies in four holes from the third put him back on track.
Large crowds continued to flock to catch a glimpse of Woods, even as he battled to stay within shouting distance of the leaders Saturday.
"I've done that very well on a number of occasions, been close to winning before and hopefully we got a great chance of winning it tomorrow". Felt a little bit more in control of my game.
South Korea's An Byeong-hun was in a pack on 208 that also included Americans Rickie Fowler, Talor Gooch and Charley Hoffman.
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Of his record eight victories at Bay Hill, Woods has led six times and was tied for the lead another time.
"It's really different", McIlroy said of the sounds that reverberate around a course when Woods is playing. "For a long time when I did kind of get out here a little bit, he was never here and it was a sore disappointment to have him not be here".
Stenson opened with a 13-foot birdie putt and answered a bogey at eight with a 30-foot birdie putt at nine.
But an errant tee shot at the par-5 16th led to a bogey and he dropped another shot at the 17th to fall well off the pace at 10 under. I don't know, I think it's gotten a little much, to be honest.
Bryon DeChambeau also sputtered early and came on strong at the end with a 7-foot eagle putt on the 16th and an approach to 4 feet for birdie on the 18th for a 66.
Whether or not Tiger Woods won the Arnold Palmer Invitational yesterday (this morning, Singapore time), the 14-time Major champion left Bay Hill knowing that he has made solid progress in his comeback from surgery.
With the Masters only three weeks off, Woods now has nine consecutive rounds of par or better - his longest such US PGA streak in more than five years. Instead of pitching out to the fairway, he hit a shot over the trees and the water that set up a two-putt birdie, and he hit sand wedge into the 18th for a 12-foot birdie putt and a 69.