Rafa Cabrera-Bello advanced into the last 16 at the WGC-Dell Match Play after halving his match against Søren Kjeldsen at Austin Country Club.
The Spaniard, who was the lowest-ranked seed in Group 12, knew a win or a half would see him go through and he was pushed all the way by the Dane.
Kjeldsen, who was already eliminated from the tournament before day three, led by one hole heading into the back nine.
Birdies on the tenth and 12th saw Cabrera-Bello move briefly ahead before Kjeldsen responded to go one up with 17 played.
Cabrera-Bello held his nerve on the final hole, driving the green before two-putting for birdie.
"Søren has been a really tough competitor today," he said. "Obviously he didn't have anything to lose, so he was playing a bit more relaxed, but you could see that he still wanted to win.
"When I saw I was one down really on 18, I told myself, 'just don't think of it as one single hole, just think that you have got two holes'. I knew I had the play-off guaranteed, so I felt like I was going to play two play-offs.
I do believe in my game. I know when I play well, I can beat almost anybody. I have done it before. Why not keep doing it this week? - Rafa Cabrera-Bello
The winner of the match between Hideki Matsuyama and Kevin Kisner needed Cabrera-Bello to lose to stand a chance of forcing a play-off but the 12th seed fell short despite his 3 and 2 win over the American.
Byeong-hun An advanced into the round of 16 with a win over Scott Piercy on the first play-off hole.
The South Korean had earlier halved his final Group 5 match with Rickie Fowler, while Piercy capitalised on Jason Dufner's shot penalty on the 18th to edge past his countryman by one hole.
In the play-off, a 131-yard approach to the green set up a three-footer to seal An's passage into the next round.
"I was three down after seven. I had a chance to close out 17, but it wasn't an easy putt, I left the door open for Rickie. It was a nice birdie to finish," said An.
He will now face another European Tour Member in Cabrera-Bello.
Sergio Garcia's 5 and 4 win over Marc Leishman was not enough to see him progress after Group 13 leader Ryan Moore beat Lee Westwood 3 and 1.
Garcia produced a moment of brilliance with a 108-yard approach to eagle the tenth and the Spaniard would not look back as he recorded another birdie on the 13th en route to victory.
Moore won three of the last four holes in his match to ensure he advanced by half a point over Garcia in the group.
Meanwhile in Group 4, 63rd seed Patton Kizzire reached the knockout stages with a 2 and 1 win over Emiliano Grillo.
Before day three, Bubba Watson looked to be in control of the group with a win and a tie to his name but was beaten by one hole by J.B. Holmes as Kizzire pipped the World Number Four by half a point in the group.