Top seed Jordan Spieth put in a solid performance to win his opening match of the WGC-Dell Match Play on Wednesday, while Rickie Fowler lost out to Jason Dufner.
Spieth won five of the first seven holes to outlast Welshman Jamie Donaldson 3 and 2 at the Austin Country Club in Texas.
However Fowler, the number five seed, struggled in his match against Dufner, despite an impressive comeback on the back nine.
Fowler rallied from three down to square his match on the 15th hole, but Dufner responded with birdies on the next two holes to beat him on the 17th.
Jason Day managed to overcome an early deficit and a back injury after closing out Graeme McDowell 3 and 2.
Day showed signs of discomfort after finding the bunker from the 16th tee, and looked far from comfortable as he later edged into the hazard, but still managed to win against his Northern Irish opponent.
Phil Mickelson, playing this World Golf Championship for the first time in five years, built an early lead against Matthew Fitzpatrick that the 21-year-old could not surmount, sealing a dominant 5 and 4 win.
Defending champion and third seed Rory McIlroy secured a 1-up victory over Thorbjorn Olesen, while seventh seed Justin Rose defeated Argentinian Fabian Gomez 2-up.
Fourth seed Bubba Watson halved his match with PGA Tour rookie Patton Kizzire, while sixth seed Adam Scott also had to settle for a halve with Thomas Pieters of Belgium.
In other results, Dustin Johnson went down to Robert Streb, and Hideki Matsuyama lost out to Rafael Cabrera-Bello.
The biggest win of the day was by Matt Kuchar, who thrashed Anirban Lahiri 6 and 5.