Jason Day suffered a back injury in his opening pool match at WGC-Dell Match Play but still managed to defeat Northern Ireland's Graeme McDowell 3&2.
The Australian world number two appeared to pick up the problem on the 16th tee and went for treatment following his victory.
Defending champion Rory McIlroy only secured his win over Thorbjorn Olesen on the last hole when the Dane bogeyed.
World number one Jordan Spieth overcame Wales' Jamie Donaldson 3&2.
Five-time major champion Phil Mickelson recorded a 5&4 victory over England's Matthew Fitzpatrick.
World number five Rickie Fowler lost to Jason Dufner, who posted a 2&1 victory, and two-time runner-up Paul Casey of England was beaten 2&1 by Thailand's Thongchai Jaidee.
England's Andy Sullivan, who recorded three European Tour wins last year, defeated Austria's Bernd Wiesberger 3&2.
The five-day tournament features the top 64 in the world. The golfers are split into 16 groups of four for a round-robin format which takes place over the first three days. The event then becomes a straight knockout at the weekend among the 16 group qualifiers.