World No. 2 McIlroy, seeking his second title in three seasons, lost 2 and 1 to Denmark's Soren Kjeldsen and Japan's Hideto Tanihara defeated fifth-seeded Speith 4 and 2.
Kjeldsen will have a rest day tomorrow as his would-be opponent Gary Woodland has withdrawn from the event for personal reasons.
However, Soren Kjeldsen, who beat McIlroy in the first round, won his second match with Emiliano Grillo and will also be awarded a walk-over against Woodland giving him an insurmountable lead in the group.
Lee Westwood was handed a win following Day's withdrawal and can force a play-off in group three by beating Pat Perez on Friday, while Kevin Na needs just half a point against Chris Wood after beating Justin Thomas in group six.
Two years ago at Harding Park, seven matches went extra holes and cut in front of matches that were ready to start.
What wound up hurting McIlroy is he didn't get to play at all.
Bay Hill victor Marc Leishman also had a chance to clinch his group if he had beaten Pat Perez, because Leishman was to face Day in the third round.
On Wednesday, thoughts of his mother again caused the Australian to cry, but this time they were tears of anguish. McIlroy had not announced if he will enter the Houston Open next week.
As if match play wasn't quirky enough, the round-robin format added a freaky element Friday at Austin Country Club.
Day's all-in approach to golf encouraged him to play in tournaments leading up to next month's Masters, the Major that Day has wanted to win more than any other since he was a small child.
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World number one Dustin Johnson continued his flawless record at the WGC-Dell Match Play on Thursday while number two Rory McIlroy was eliminated without even setting foot on the course.
Rahm kept his golf ball dry to move to dormie with five holes to play.
Noren beat Bernd Wiesberger 3-and-2 his second straight victory.
By losing their matches Thursday, they were among at least eight players mathematically eliminated from winning their group and advancing to the knockout stage on the weekend.
"It happens", Mickelson said. McIlroy faced Woodland in the championship match when he won the Match Play in 2015 at Harding Park. So much depends on Friday, how surgery goes to remove a mass that Day said was 3 to 4 centimeters.
Dustin Johnson had another easy time as he tries to get in position for his third straight victory, but he still has one more match to claim his group.
Casey shrugged off the windy conditions now that he was in familiar match-play territory in Friday's only meeting of 2-0 players.
"Obviously, to shoot the score I shot today you have to putt well", Mullinax said.
Mickelson last made it past the third round when the Match Play was single elimination.