The world number two declined to stop and chat with reporters but his agent later said Day expected to play his next match on Thursday.
"Jason tweaked his back (driving) on hole No. 15 and had some work done post-round. He is pleased with the outcome of the match and is getting prepared to play tomorrow," his agent Bud Martin said in a statement.
World number one and local favorite Jordan Spieth, who played college golf at the University of Texas in Austin, led from start to finish against Jamie Donaldson of Wales in a 3&2 win.
"I felt comfortable," said Spieth, who in contrast to most of the rest of the field is familiar with the course.
Third-ranked Rory McIlroy of Northern Ireland survived a tight match against Thorbjorn Olesen for a 1-up win clinched after the Dane made a mess at the last, including a shanked chip shot from greenside rough.
"The quality of golf out there wasn't that good. I feel like it's hard for the quality to be good because the wind was so gusty," said McIlroy. "I didn't have my best stuff today but I hung in there. Just happy to get the win."
Twice Masters winner Bubba Watson went to the final hole 1-up but settled for a half when fellow-American Patton Kizzire birdied the last. Also halving his opener was Adam Scott, who led 2-up before birdies at 16 and 17 by Belgian Thomas Pieters.
World number five Rickie Fowler lost a duel against his friend Jason Dufner, who posted a 2&1 victory, while Englishman Paul Casey, twice a runner-up in the event, lost his match with 46-year-old Thongchai Jaidee of Thailand by the same score.
Other favorites to fall included Dustin Johnson, who lost to fellow-American Robert Streb 3&2 and American Jimmy Walker, beaten 2&1 by Kiradech Aphibarnrat of Thailand.
Defeat did not eliminate competitors as Wednesday was the first of three days of group play, with the winners of the 16 four-man groups advancing to single-elimination this weekend.
Other winners included Spaniard Sergio Garcia over Ryder Cup teammate Lee Westwood of England, Charl Schwartzel of South Africa against New Zealand's Danny Lee, and Phil Mickelson, who thumped 21-year-old Englishman Matthew Fitzpatrick 5&4.
(Reporting by Larry Fine in New York; Editing by Frank Pingue/Greg Stutchbury)
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