Australia's two-time champion beat Frenchman Victor Perez 2&1 at Austin Country Club to go top of Group 9 with a 2-0 win-loss record.
"Today was a little bit scrappy but coming off yesterday's round I felt pretty good about my game," Day said.
"I was with my coach last week and I'm just trying a few different things with my swing and it's a good test to see how well it copes under pressure. It feels like you're playing Sunday pretty much every round here.
"So I'm very happy."
Day can secure a place in the last 16 with a win or a tie in his final group match on Friday against two-time major winner Collin Morikawa, who squared his second match on Thursday with Canadian Adam Svensson.
Fellow former Australian world No.1 Adam Scott finished 1 down against American Sam Burns to lose control of his destiny in Group 13.
Scott (1-1) needs to beat Adam Hadwin (0-2) next and hope Burns (2-0) loses to Seamus Power (1-1) to force his way into a sudden-death playoff to make the knockout rounds.
Scott could have been in a much better position had he not driven into the hazard on the last hole to gift Burns the match.
But having trailed seven times during the day, and only hitting the lead for the first time on the 18th in his opening win over Power, the former Masters champion eventually paid the price for living dangerously at this cut-throat event.
Fellow Australians Min Woo Lee (1-0), Lucas Herbert (1-0) and Cam Davis (0-1) are also playing their all-important second matches on Thursday.
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