MARANA, February 20, 2014 (AFP) - England's Rose, the reigning US Open champion, was the last lead man in his quarter of the bracket to fall, being taken out in 20 holes by four-time major winner Ernie Els of South Africa.
After winning 17 to square the match and halving 18 with pars, Els matched Rose with a nine-foot birdie putt on the first extra hole.
Els lofted a pitch to three feet on the last hole to win as Rose took two shots to escape a bunker.
"It was one of those once in a lifetime shots really," Els said. "I was in the downhill on the back of the bunker. I caught it a smidge thin and it came out perfectly. It was an impossible shot but obviously it was the right one at the time."
Els reached a third-round matchup with 2013 PGA Championship winner Jason Dufner, who eliminated Italy's Matteo Manassero 2 and 1.
South Africa's Louis Oosthuizen, the 2010 British Open champion, dispatched Sweden's third-ranked Stenson 4 and 3 while American Harris English defeated McIlroy in 19 holes.
Stenson's defeat continues a trend in which the overall highest-ranked starter at the $9 million event has not gone beyond the second round since 2008.
Oosthuizen never trailed, going 2-up after an 18-foot eagle at the second. He took the 12th when Stenson missed a 16-foot par putt and then sank a 20-foot birdie at 15 for the triumph.
"I played pretty solid," Oosthuizen said. "I just kept it together. Just played solid and made nice putts on the back nine."
Oosthuizen will next face American Webb Simpson, who ousted countryman Brandt Snedeker 4 and 3, and could meet Australian second seed Jason Day in the quarter-finals.
Day needed 22 holes to eliminate American Billy Horschel. Day, third at the event last year, next meets South African George Coetzee, who beat American Patrick Reed in 21 holes.
"It was a tough one," Day said. "Doesn't matter how you get it done, find a way to win."
McIlroy took a bogey at 10 and two penalty strokes in the Arizona desert on 11 to fall 2-down, but battled back with three birdies to go 1-up after 16, only to have English sink a 19-foot birdie at 17. McIlroy fell by making a double bogey on the first extra hole.
English next faces Jim Furyk with that winner to meet either Sergio Garcia or American Rickie Fowler.
Garcia, another second seed, outlasted American Bill Haas 3 and 1 and Fowler edged US compatriot Jimmy Walker 1 up, beating the only winner of three US PGA Tour events this season.
Northern Ireland's Graeme McDowell, two down with four holes to play, edged Japan's Hideki Matsuyama 1 up.
"I'm really quite lucky to be standing here right now," McDowell said.
McDowell, who was 3-down with three to play before rallying to beat Gary Woodland in round one, pulled level for the first time against Matsuyama with a five-foot birdie at the 1th then won with a seven-foot par save at 18.
"Why do it the easy way when the hard way will do?" McDowell said. "I got off to a slow start again. I tried to execute my game, not make any mistakes and he kind of played the same."
McDowell, the 2010 US Open champion, booked a third-round date with American Hunter Mahan, the 2012 Match Play winner and 2013 runner-up who ousted South African Richard Sterne 2 and 1.
Also through to the last 16 at the 64-player event is Victor Dubuisson, who dispatched Swedish 15th seed Peter Hanson 3 and 1.
"I started the first few holes and I made some good birdies," the Frenchman said. "Then he made three birdies and we were all square. Then I decided just don't watch him play, just play my stroke play and try to make some birdies."
Next up for Dubuisson is American Bubba Watson, last week's PGA winner at Riviera, who beat Swede Jonas Blixt 2 up.
Results on Thursday from the second round of the $9 million World Golf Championships Match Play Championship (x denotes seed):
Bobby Jones division
Louis Oosthuizen (RSA x8) bt Henrik Stenson (SWE x1) 4 and 3
Webb Simpson (USA x5) bt Brandt Snedeker (USA x4) 4 and 3
Jason Day (AUS x2) bt Billy Horschel (USA x10) 22 holes
George Coetzee (RSA x14) bt Patrick Reed (USA x11) 21 holes
Ben Hogan division
Harris English (USA x9) bt Rory McIlroy (NIR x1) 19 holes
Jim Furyk (USA x5) bt Charl Schwartzel (RSA x4) 3 and 2
Sergio Garcia (ESP x2) bt Bill Haas (USA x7) 3 and 1
Rickie Fowler (USA x14) bt Jimmy Walker (USA x6) 1 up
Gary Player division
Ernie Els (RSA x8) bt Justin Rose (ENG x1) 20 holes
Jason Dufner (USA x4) bt Matteo Manassero (ITA x12) 2 and 1
Matt Kuchar (USA x2) bt Ryan Moore (USA x7) 1 up
Jordan Spieth (USA x3) bt Thomas Bjorn (DEN x6) 5 and 4
Sam Snead division
Hunter Mahan (USA x8) bt Richard Sterne (RSA x16) 2 up
Graeme McDowell (NIR x4) bt Hideki Matsuyama (JPN x5) 1 up
Victor Dubuisson (FRA x7) bt Peter Hanson (SWE x15) 3 and 1
Bubba Watson (USA x3) bt Jonas Blixt (SWE x11) 2 up