MARANA, February 21, 2014 (AFP) - McDowell, the 2010 US Open champion from Northern Ireland, won the 17th and 18th holes to square the match, sank a 19-foot par putt on the 20th hole and then sank a 14-foot birdie putt on the last hole to advance.
"I genuinely thought I was done this time. I didn't think there was any way back," McDowell said.
"Nine lives have been used up and then some."
McDowell has played 58 holes and never led in any match until the final hole.
"I'm not embarrassed, but I just feel like I'm robbing these guys," McDowell said.
Mahan, the 2012 Match Play winner and 2013 runner-up, staged a rematch of his epic 2010 Ryder Cup singles showdown with McDowell, who beat the American 3 and 1 at Celtic Manor to clinch the trophy for Europe.
McDowell advanced to a quarter-final matchup against France's Victor Dubuisson who upset 2012 Masters winner Bubba Watson 1 up, downing him five days after the American's triumph at Riviera, his first since taking the green jacket at Augusta National.
"We didn't play very well, both of us, but I managed to save some great pars to win," the Frenchman said.
South African Ernie Els hit a wedge shot two feet from the cup at the 18th and made the putt to defeat 2013 PGA Championship winner Jason Dufner 1 up and book a last-eight match against rising US star Jordan Spieth, a 2 and 1 winner over countryman Matt Kuchar.
"I'm glad to go through," Els said. "The first couple of holes I made some mistakes and then he made a couple of mistakes on five and six to give me two holes. And then we played a little bit better."
South African Louis Oosthuizen beat American Webb Simpson 5 and 4 in a third-round matchup of major winners to book his quarter-final spot.
"I made quite a few birdies coming in," said Oosthuizen. "He put himself in a few tough spots to make bogeys and pars and I just for some reason made a few putts and hit a lot of birdies."
Next up for Oosthuizen will be Australian Jason Day, who ousted South African George Coetzee 3 and 1.
The Aussie, who finished third at last year's Match Play, never trailed and birdied four of the last seven holes to advance.
Americans Jim Furyk and Rickie Fowler booked a quarter-final matchup with 1-up triumphs, 2003 US Open winner Furyk dispatching countryman Harris English and Fowler ousting Spanish star Sergio Garcia.
After Garcia felt guilty about the long pause before a putt dropped at the sixth hole, he conceded Fowler a difficult 17-foot par putt at the seventh.
"I don't regret it at all," Garcia said. "This is a gentleman's game and lately it hasn't felt like it has been that. This is the way I was brought up."
Garcia led all the way until the 16th as Fowler birdied that and sank a four-foot birdie at 18 for the victory.
Furyk, who at 43 is 18 years older than Fowler, was 3-down after six holes but squared his match with a nine-foot birdie putt at 12 and took his first lead with English made bogey at 14. English leveled with a birdie at 15 but Furyk chipped in from 30 feet at 16 and held on for his first trip to the Match Play last eight.
"I had been in this position before," Furyk said. "I was able to dig my way out."
Results on Friday from the third round of the $9 million World Golf Championships Match Play Championship (x denotes seed):
Bobby Jones division
Louis Oosthuizen (RSA x8) bt Webb Simpson (USA x5) 5 and 4
Jason Day (AUS x2) bt George Coetzee (RSA x14) 3 and 1
Ben Hogan division
Jim Furyk (USA x5) bt Harris English (USA x9) 1 up
Rickie Fowler (USA x14) bt Sergio Garcia (ESP x2) 1 up
Gary Player division
Ernie Els (RSA x8) bt Jason Dufner (USA x4) 1 up
Jordan Spieth (USA x3) bt Matt Kuchar (USA x2) 2 and 1
Sam Snead division
Graeme McDowell (NIR x4) bt Hunter Mahan (USA x8) 21 holes
Victor Dubuisson (FRA x7) bt Bubba Watson (USA x3) 1 up