For the third straight year in Match Play, the defending champion will not make it to the weekend.
Day was also eliminated Thursday after his second-round loss to Henrik Stenson. Day lost the first two holes and played the entire round from behind before Stenson closed it out 4 and 3. Day lost his opening match Thursday to Jim Furyk.
Johnson lost to Branden Grace in a tight match that wasn't decided until Johnson pulled a long birdie from the fringe on No. 18 wide left. The loss leaves Johnson 1-1 after two rounds and needing to beat Hideki Matsuyama on Friday to have a chance to advance.
Furyk will meet Stenson on Friday with the winner advancing to the weekend elimination rounds.
"It's going to be a tough one again,'' Stenson said. "Jim, I don't think he's given away an easy bogey since 1994 or something.''
Furyk wasn't planning to be in Texas this week. It wasn't until a runner-up finish in The Players Championship two weeks ago -- he was among the last into the field at the TPC Sawgrass -- that allowed him to crack the top 64 in the world to qualify for Match Play.
A victory Friday is likely enough to get him into the Masters.
"I guess I'm not really upset with anything right this second,'' Furyk said. "I feel pretty consistent and pretty solid throughout my game.''
Meanwhile, Na did not go quietly against Jordan Spieth. He was 6 down with six holes to play before winning the next three holes. Na had a 4-foot birdie putt to cut into the deficit even more but missed it. Spieth won 3 and 2.
Abraham Ancer delivered the first victory among 32 matches at Austin Country Club with a 3-and-2 victory over Cameron Smith. Moments later, Paul Casey missed a 7-foot par putt and had to settle for a tie with Charles Howell III.
That eliminated Smith from Group 10, one year after the Australian reached the quarterfinals.
Patrick Reed lost the 18th hole at Austin Country Club when his pitch went over the back of the green, and Shane Lowry chipped to birdie range. The match ended in a tie, which eliminated both from advancing out of their group.
Sergio Garcia romped past Andrew Putnam in the other Group 16 match, his second win. That means Reed and Lowry, even if they were to win Friday matches, cannot reach the two points Garcia already has.
Meanwhile, Justin Rose delivered the best comeback. He was 3 down with four to play against Eddie Pepperell when he rallied to earn a halve with birdies on the last two holes. Cheering him along outside the ropes was Mark "Fooch'' Fulcher, his caddie who is recovering from a heart operation and worked nine holes of practice as he readies his return to Rose's bag at the Masters in two weeks.
"He's been walking on the sidelines and gave me, 'Come on, Rosie.' I could tell he hadn't given up on me,'' Rose said. "Picked me up a little bit and made me dig a little deeper possibly.''
The Associated Press contributed to this report.