Both players recorded opening rounds of 1 under par 70 and find themselves inside the top 10 at the completion of a demanding opening day at the Innisbrook Resort at Palm Harbour near Tampa.
Two late bogeys were a disappointing way to finish for Scott after he had moved within one of the leader, Corey Conners of Canada.
But after the improvement the Queenslander displayed when finishing strongly at the Honda Classic two weeks ago, things are very much heading in the right direction after an indifferent start in his opening two starts of the year.
Scott's game, which had suffered through off-course distractions for much of 2017, appears to be on the way back after slipping to his current 58th position in the world ranking.
Woods' round was sprinkled with some of the brilliance of the past and after working his way within two of the lead through 11 holes he would drop shots at the 12th and 13th before a remarkable par save at the 16th was followed by a brilliant birdie at the par-three 17th.
"It was really brutal out there," said Woods referring to the windy conditions. "We [Woods, Stenson and Spieth] as a group got fooled a lot today.
"I'm still working on it and it is getting a little better piece by piece and this was a very good test of all the things I am trying to implement."
It was Woods' first visit to this event and this golf course in 22 years providing even further merit in his performance.
26-year-old Conners is in his rookie season on the PGA Tour after playing the MacKenzie Tour in Canada and then the Web.Com Tour last year.
Conners, who has yet to win on any of the tours on which he has played and is currently ranked outside the top 600 in the world, has missed only one cut in nine starts on the PGA Tour in the 2017/2018 season but this is by far his most impressive start.
Conners leads by one over Whee Kim, Kelly Kraft and Nick Watney.
Of the Australians other than Scott, Cameron Smith had even par 71, Rod Pampling and Aaron Baddeley opened with 72, while Geoff Ogilvy and Greg Chalmers struggled to rounds of 76.
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