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Rory McIlroy fought back from two down to defeat Thorbjorn Olesen at the WGC-Dell Match Play at Austin Country Club.
The defending champion found himself two down after 13 holes, but Olesen bogeyed three of the last five holes to gift McIlroy the win.
"I do feel fortunate. I was not up until the final hole and feel a little bit bad for Thorbjorn. He played pretty solid and just had a bad finish and opened the door for me," McIlroy told Sky Sports.
"After I went two down after 13 a switch sort of flipped on for me and I started to hit some quality shots. I was a little flat for the front nine but coming in I started to hit some good quality shots and I am happy with that."
Jason Day overcame a back problem to defeat McIlroy's compatriot Graeme McDowell 3&2.
McDowell took an early lead over the Australian, moving two up through four holes, but Day recovered despite picking up a back injury during his closing few holes and he headed straight for treatment at the end of his match.
World number one Jordan Spieth also opened with a win as he defeated Jamie Donaldson 3&2, while Phil Mickelson did not lose as hole on his way to a 5&4 win over England's Matt Fitzgerald.
Sergio Garcia and Lee Westwood produced one of the battles of the day, taking their match to the 18th hole before the Spaniard eventually claimed the win.
Garcia had been two up after three but lose the next four to slip behind his former Ryder Cup team-mate. However, he then won four holes in succession.
"It was very, very funny. Lee said to me on 17, 'We are gelling well!' It would have been better in a fourball," he told Sky Sports.
"It was very up and down. I started very well and he hit a couple of poor shots, then he got on a great run and the last three or four holes he was making birdie or I was. I'm very happy with the putt I made on 18 to get the win."
World number five Rickie Fowler lost to Jason Dufner 2&1, while Shane Lowry was beaten by Martin Kaymer.