Ahead for most of their clash for a place in the quarter-finals at Finca Cortesin, Poulter lost the 14th and 15th to be pulled back to all square, but then hit his tee shot to three feet on the short 17th.
Westwood, winner of his last two tournaments in Indonesia and Korea, was bunkered in two at the par five last and although he splashed out to three feet and holed for birdie, Poulter had chipped closer and made it for a one up win.
Earlier Graeme McDowell won the all-Irish battle with Rory McIlroy 3 and 2, while Donald was two down with three to play against Swede Johan Edfors, but won the next two, halved the last in birdies and then showed again on the first extra hole that he is the best bunker player in the world.
While Edfors could not get up and down, Donald splashed out to two feet and so made certain of an eighth successive top-ten finish.
He needs to win the title, though, to replace Westwood - and, of course, to make it a World Match Play double after his triumph in Arizona in February.
Next up for him is Masters Tournament winner Charl Schwartzel, who matched the closing eagle of defending champion Ross Fisher to win one up.
Kaymer, beaten by Donald in the final in Tucson, also has to lift the trophy to return to number one, but he stayed on course for that with a 3 and 2 victory over Dane Søren Kjeldsen.
He then faced Spain's Alvaro Quiros, while McDowell took on Belgian Nicolas Colsaerts and Poulter faced another Ryder Cup teammate in Italian Francesco Molinari.
There was no hiding how annoyed McIlroy was as he allowed McDowell to get away from him.
The 22 year old missed two good opportunities to reduce the deficit at four down.
He got two back with birdies, but McDowell finished him off after holing from the fringe at the 16th - again from further away than his opponent.
It was a clash, of course, between not just Northern Ireland's two leading players - McDowell is ranked fifth in the Official World Golf Ranking, McIlroy sixth - but also Ryder Cup partners and close friends.
McIlroy's problems began immediately when he three-putted to fall behind and it was also clear there that he had no intention of being generous.
After being asked to hole from around three feet there, McDowell was made to putt from even closer in at the next for a half.
McIlroy hit his second into the lake on the long third to go two down and the gap went to three when he three-putted the par five eighth.
He did manage an 18 footer from just off the ninth green, but it was only for a half with McDowell holing from five feet and even though he was the closer of the two at the 11th McIlroy was the one to miss.
McIlroy said: "I missed five chances in the middle that really cost me. It was a great battle, but I couldn't get a putt to go in.
"I was getting very frustrated - when you are going against someone of that calibre you need to take your chances."
Westwood was left to reflect on what might have been after his loss.
"You know he's not going to hit it great, but he's going to make a lot of putts and get up and down from everywhere," he said.
"I didn't make any putts, he did and he had a couple more breaks than me. That's the frustrating thing about match play and especially 18-hole match play - sometimes it's not reflective of how the players are playing.
"He didn't hit a great shot at 17. He wasn't aiming at the left fringe and it comes down to two foot. You have those days.
“My game is in great shape - I played lovely today. I made two bogeys on the par threes, but around in 67, something like that. So 19 under par for 45 holes and going home -that's how match play is.”
Poulter teed off again and birdied the first to lead Molinari.
Donald birdied the third and fourth, but the first was for a half and the next left him one down as Schwartzel eagled.
Donald and Kaymer were on course for a semi-final clash, both one up with eight and seven holes to play respectively.
McDowell, though, was two down after eight and Poulter's bogey at the seventh brought him back level with Molinari.
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