Thomas is the only top-10 seed to make the quarter-finals, after Spanish seventh seed Sergio Garcia was sent packing by American 45th seed Kyle Stanley, who pulled off a minor upset with a 3&1 victory.
Oosthuizen was not going out without a fight, though, and recorded birdies at 14 and 16 to take the match to the wire.
Bogeys by Kisner at the par-5 third and par-3 fourth staked Watson a 4-up lead and a concession birdie by bogey-bound Kisner followed at five.
But his victory appeared to affect his memory, Poulter praising Oosthuizen for being a Masters victor - a tournament he never won.
(35) Watson vs. (64) Julian Suri, halved: Needing just a half-point to advance, but two down with two to go, Bubba stuffed his tee shot on 17, then hit his driver pin-high on the home hole. I'll do my bit and focus better, " Poulter said.
Bubba Watson will be his opponent in Sunday's first semi-final after the two-time Masters champion beat Thailand's Kiradech Aphibarnrat 5&3.
Thomas (3-0), ranked No. 2 in the world, can become No. 1 by winning the tourney.
Boko Haram returns Nigerian kidnapped schoolgirls say witnesses
Negotiations through a back-channel led to the release of 101 Dapchi girls and a boy, the Nigerian government said Wednesday. President Muhammadu Buhari's media aide confirmed on Wednesday that the girls were being transported to meet their families.
And if you're looking for a Texas connection in what's left of this year's Dell Match Play, the closest one you'll find is in Thomas.
Watson was never behind and despite Aphibarnrat managing to get their match back to all square at the ninth, the American then won four holes in succession from the 10th hole and all with birdies to race to 4-up through 13 holes and with Aphibarnrat conceding the 15th for a Watson victory.
Turns out Poulter still needed to win one more match, and he received a text message letting him know where he stood.
But despite not feeling 100 percent early on, Thomas has been nothing short of stellar this week at Austin Country Club.
Noren now has won seven of his last eight matches in his event, his only loss coming to Johnson in the quarterfinals previous year.
Justin Thomas showed no signs of slowing down in his quarterfinal thrashing of Si Woo Kim.
Watson won for the second time this year, adding him to the list of favorites for the Masters. His 12-foot birdie putt to win with the 13th again narrowly missed, and the force with which Thomas whipped the putter shaft onto his shoulder showed his frustration. Watson next faces Harman, a match of Georgia lefties. Noren missed an 8-foot birdie putt on No. 18 that would have closed out the match, then opened the door for Kisner with a poor eagle putt on the first extra hole that barely stayed on the green.