Fowler survived a tough match and secured his spot for the weekend.
Spieth rolled to another easy victory and still faces the prospect of going home Friday.
Even with a round-robin format, this World Golf Championship added another layer of quirkiness. Spieth, top-seeded Rory McIlroy, Gary Woodland and Bubba Watson are all 2-0 and face elimination matches. Fowler and John Senden have won their groups and next play what amounts to a practice round in the middle of a tournament.
Fowler was all square in his match with Shane Lowry of Ireland when he made putts of 15, 18 and 30 feet -- all to halve the hole -- before making a birdie on the 18th to win his second match and lock up the best record in his group to advance.
"Definitely a stress reliever right there," Fowler said.
"Must be nice," Spieth said under his breath with a smile when told that Fowler was already in the round of 16.
The 21-year-old Texan had little room to talk. He is looking as dominant as his week at Augusta National, finishing off a 4-and-3 victory over hard-luck Matt Every with 10 straight one-putt greens that totaled about 120 feet. Four of those putts were to halve the hole, including a 20-footer at No. 8 and an 18-footer at No. 14 that swirled around the cup.
"After the one on No. 8 (20 feet), which was to tie the hole, he said, 'When are you going to stop doing that?'" Spieth said. "And then after I made the par putt on 14 (18 feet for a halve), I could see he was upset. And if I were in his position, I would have been very upset. Because that was bogus."
"It's going to be hard to keep making this many putts and this many birdies," Spieth said. "And I feel like I'm truly going to need that to beat him."
McIlroy went the distance to beat Brandt Snedeker, while Billy Horschel had no trouble dispatching Jason Dufner. McIlroy and Horschel are both 2-0 and play Friday to determine who advances to the weekend.
"It's win or go home," McIlroy said. "So it's back to the usual format."
Senden joined Fowler as the only two players to lock up spots in the round of 16, when the Match Play returns to single elimination. He easily handled Bill Haas, and won his group when Henrik Stenson beat Brendon Todd. Senden already has beaten Stenson and Haas, who each have a 1-1 record.
Otherwise, the second day at TPC Harding Park brought out a strange element for match play -- scoreboard watching.
J.B. Holmes went 19 holes to beat Russell Henley and then stayed on the course to watch the match behind him. He knew Brooks Koepka had to win or else Holmes would be eliminated. Koepka won the last three holes and wound up beating Marc Warren of Scotland.
In other matches:
• Watson and Louis Oosthuizen each won their matches to set up a win-or-go home match Friday in their group. Watson beat Keegan Bradley, now how has lost his last seven singles matches in Match Play, the Ryder Cup and Presidents Cup.
• Woodland put away Poulter, the Ryder Cup wizard who now has lost his last three matches in this tournament. That means Woodland and Webb Simpson, who beat Walker, will play Friday for the right to advance.
• Thongchai Jaidee defeated Jim Furyk, and George Coetzee rallied to beat Martin Kaymer. Everyone in that group is 1-1, so a head-to-head tiebreaker will be used for winners to see who advances. That's also the case in the group with Sergio Garcia, Bernd Wiesberger, Tommy Fleetwood and Jamie Donaldson.
Fowler knew he would win his group provided Harris English beat Graeme McDowell, because Fowler had already defeated English. McDowell had a 3-up lead until English rallied to win five out of six holes for a 2-and-1 victory.
"Obviously, I still want to go out and play a good match and win the match," Fowler said. "In a way, it will give me time to work on stuff and ... see if we can tighten the game up a little bit."