Jason Day admitted he had considered withdrawing from the WGC-Dell Match Play before his 5&3 victory over Thongchai Jaidee.
Day injured himself in the closing stages of his 3&2 victory over Graeme McDowell in their group match on Wednesday, leading to doubts as to whether he'd be able to continue in the tournament.
The Australian's agent later issued a statement saying the US PGA champion had "tweaked" his back on the 15th tee but was preparing for his clash with Jaidee, who had beaten England's Paul Casey in the opening matches.
And despite appearing to rub his back before hitting his tee shot on the first, the world No 2 promptly drove the green on the 391-yard par four and holed from 12 feet for an eagle to win the hole.
Day reached the turn two ahead and kicked off the back-nine with successive gains, before completing a convincing win with three holes to spare by holing a seven-foot birdie at the 15th.
"It definitely felt a lot better," Day told Sky Sports. "I wasn't nursing it anywhere near it anywhere near as much as what I was doing yesterday.
"The biggest thing for me this morning was to see if I was protecting it and if I had been I'd have pulled out and focused on Augusta.
"I came out a little sore but was hitting it at full stride as it showed at the first when I drove the green."
All of the top four seeds won their matches on Thursday, with world No 1 Jordan Spieth easing to a 5&4 win over Victor Dubuisson and defending champion Rory McIlroy seeing off Smylie Kaufman 3&1.
The Shriners Hospitals for Children Open twice held a narrow advantage over McIlroy, who reached the turn one ahead before winning three holes in-a-row from the 13th.
McIlroy completed the victory when Kaufman found more trouble on the 17th and conceded the hole, leaving the Northern Irishman facing a group decider against Kevin Na on Friday.
After admitting to feeling fortunate to beat Olesen on Wednesday after the Dane squandered a two-hole lead with five to play, McIlroy told Sky Sports: "I played much better today.
"There were still a couple of mistakes in there, but for the most part I hit better shots.
"The course played differently today with the change in wind direction, but I think I made four birdies in the first six holes and a couple more on the back nine. The quality of golf was much better.
"I needed that as Smylie (Kaufman) played quite solidly. I was able to play well when I needed to and win those holes on the back nine."