At Celtic Manor in Wales, Mahan was well short on the par-3 17th, flubbed a chip, and conceded a par to McDowell that gave Europe the 14 1/2 points it needed to take back the cup.
''It's definitely time to stop playing the replay, that chip shot that he hit on 17 at Celtic Manor in 2010,'' McDowell said. ''The guy is a quality, quality golfer. He hit some great chip shots today. I said to The Golf Channel this morning, 'His career is not going to be defined by that chip shot, no chance.'
''He's won two WGCs since then. He's a quality golfer, and probably deserved to beat me today. But this game doesn't give you what you deserve sometimes.''
McDowell, from Northern Ireland, also rallied to beat Gary Woodland and Hideki Matsuyama in the first two rounds.
''Obviously, I'm holing some very important putts that I really can't give my normal reactions to, because I can scarcely believe what's going on,'' McDowell said. ''Embarrassed is the wrong word. I'm not embarrassed, but I just feel like I'm robbing these guys.''
McDowell will face Victor Dubuisson in the quarterfinals. Dubuisson beat Riviera winner Bubba Watson 1 up.
FATHER KNOWS BEST: Mike Furyk gave son Jim some good advice about playing Dove Mountain.
''I think Dad was just kind of telling me not to get out of my own game, not to try to change my style or try to hit the ball higher or farther, just stick with what got me here, do what I usually do well and just try to shoot a number and see what happens,'' Furyk said.
The 43-year-old former University of Arizona player advanced to the quarterfinals, beating Harris English 1 up on Friday. Furyk chipped in for birdie on the par-3 16th to take the lead, matched English with a birdie on 17 and halved the 18th with a par.
''That's a difference in the match,'' Furyk said about the chip on 16. ''That ball doesn't go in, it might go 10 feet by and I might be 1 down going to 17 rather than 1 up. I feel fortunate it hit the center of the pin and went in.''
He reached the quarterfinals for the first time in 14 appearances in the event.
''I've never made it to the weekend at this event, so new territory for me,'' Furyk said. ''I went to school here. I've got a lot of support out there. Finally, this week, I'm giving them something to cheer for.''
Furyk will face Rickie Fowler, a 1-up winner over Sergio Garcia.
With Furyk facing Fowler on Saturday, at least one American will be in the semifinals. U.S. players were 1-2 against European opponents on Friday and are 15-9 in the first three rounds.
American players have swept the first 13 events in the PGA Tour's new wraparound season that started in October.
Only two of the 19 newcomers - Spieth and France's Victor Dubuisson - reached the quarterfinals. Spieth will face Ernie Els, and Dubuisson will play Graeme McDowell.
DIVOTS: Jordan Spieth ended Matt Kuchar's event winning streak at eight matches, beating the defending champion 2 and 1. Kuchar dropped to 17-4 in the tournament. ... The third-round losers received $148,000. The winner will get $1.53 million from the $9 million purse. Second place is worth $906,000, third $630,000, and fourth $510,000. The quarterfinal losers will get $280,000.