The 14-time major champion carded a one-under-par 70 to be tied for eighth in Palm Harbor, Florida on Thursday.
Woods, whose latest comeback to the sport has been progressing well, is set to take part in this week's Valspar Championship and was delighted to see his long-time rival secure his first landmark win since claiming the Open at Muirfield back in 2013.
Considering swirling winds made scoring hard (Woods' playing competitor Jordan Spieth shot 5-over 76), Woods' first effort at the Valspar was solid.
"Knowing his nature that he's displayed over the last 20 years, it still wouldn't be surprising if, come Masters time, he's in the hunt on Sunday and that's pretty wonderful to say".
"I'm not looking at it like that", said Woods.
Quotable: "I usually got a good memory, I guess, so I take good notes and kind of remember what you want to do on each hole". Today, made a couple of birdies, all of a sudden that puts me fourth, fifth right away. Stenson had a three-over 74, while Spieth fared even worse with a 76.
"I'm able to play more feel golf than just trying to figure out how to play golf again".
Woods made five birdies and four bogeys over the par-71 course, including a 5-iron to a few feet at the par-3 17th to join just 26 other players under par on the Copperhead course.
While Shane Lowry is in a promising position after Friday, Padraig Harrington endured another tough day, hitting a two over par 73 which leaves him at seven over par for the championship. He ranks 23rd in SG: Tee-to-Green, 14th in SG: Approach, 20th in BoB Gained, 18th in Birdies Gained, 7th in Bogeys Avoided, and 38th in Fairways Gained.
Elsewhere in the field, world number four Jordan Spieth finished his second round five over and looks certain to miss the weekend with the projected cut at two over.
It made for an awkward stance to say the least and Woods would make contact with the tree as he made his escape, but luckily there was no serious injury.
"I'm pleased with every aspect of my game", he told reporters.
Asked if he is inspired more by the younger generation winning tournaments or the likes of Mickelson, Woods added: "It's both".
While replays seemed to show Woods' hand taking the brunt of the impact with the tree, after the round he explained that the collision was felt a little higher.
Windows 10 S Coming soon to all editions of Windows 10
Further, Joe Belfiore stated that there was confusion about this version of the OS from Microsoft's partners and consumers. Microsoft today released a new Cumulative Update for Windows 10 devices running Creators Update aka version 1703.
Fortnite Battle Royale officially coming to iOS and Android
An Invite Event will go live on Monday, allowing iOS users to try to get into the first early waves of the game's player base. Fortnite and its Battle Royale version are one of those overnight success stories that nearly catches everyone by surprise.