Matthew Fitzpatrick will face Kevin Na in a play-off to decide who progresses from Group 6 at the WGC - Dell Technologies Match Play at Austin Country Club.
Na had two wins from his first two matches and when he was four up after seven holes needing just a half against Chris Wood, his progress to the last 16 looked assured.
But Wood won seven of the next eight holes with the help of four birdies and an eagle to take the match 2 and 1, meaning the winner of the clash between Fitzpatrick and Thomas would make a play-off.
Thomas was two up with five up to play but Fitzpatrick birdies on the 14th, 15th, 16th and 17th handed the Englishman a 2 and 1 win.
The winner of the play-off between Fitzpatrick and Na will face another play-off winner, with Bill Haas and K.T. Kim squaring off later in Group 11.
Lee Westwood beat Pat Perez 2 and 1 in Group 3 to force a three-man play-off with the American and Marc Leishman.
The winner will face Phil Mickelson in the last 16, the left-hander maintaining his 100 per cent record in Group 14 with a 6 and 5 win over JB Holmes.
Na took advantage of a bogey-double-bogey start from Wood to quickly move two up and birdies on the fourth and sixth had the new European Tour Member in total control.
A bogey on the eighth saw him drop back and when Wood birdied the ninth, that triggered a brilliant run as he BMW PGA Championship winner went birdie-par-eagle-birdie-par-birdie.
A Na gain on the 16th offered some hope before the 17th was halved in pars.
Fitzpatrick had won the first against Thomas but the American hit back with wins on the sixth, ninth and tenth and remained two up with five to play before the three-time European Tour winner's big finish.
Danny Willett found his form to beat Russell Knox 4 and 2 in Group 11, meaning a win for Haas against Kim would force a play-off, with the American prevailing 4 and 2.
Westwood knew only a win would do against Perez and he duly provided in a nip-and-tuck battle.
The players traded birdies on the fifth and sixth, and eighth and ninth with Perez the man to fight back each time, before Westwood birdies on the 12th and 13th provided some breathing room.
In the other Group 14 match, Si Woo Kim beat Daniel Berger one up.
