Campbell made it four straight rounds going the distance, holding off Stephen Ames for a 1-up victory that put an American in the semifinals for the ninth straight year in this World Golf Championship.
He'll face Ogilvy, the defending champion who won his 10th consecutive match by easily beating Paul Casey of England.
In other quarterfinal matches on a clear but frosty morning in the high desert, Trevor Immelman of South Africa made eight birdies to beat Justin Rose of England, 5 and 4; and Henrik Stenson of Sweden, so cold he took a jog around the practice range to loosen his limbs, pulled off an unlikely victory over Nick O'Hern by saving par from the desert for a 1-up victory.
It was the third time O'Hern has lost in the quarterfinals. His only consolation is becoming the first player to beat Woods twice in match play as a professional.
O'Hern beat Woods in 20 holes in the third round Friday, ending Woods' PGA Tour winning streak at seven and leaving the weekend to a group of players with only one major champion (Ogilvy) among them.
Stenson provided the dramatics on a chilly morning, hitting his tee shot into the base of a cactus on the 18th hole with his match even against O'Hern. He took a penalty drop, then hit a wedge off the firm desert sand to 2 1/2 feet for par. O'Hern was short of the green, pitched some 4 feet by and missed his par putt to lose the match.
The start was delayed by nearly an hour because of sub-freezing temperatures at The Gallery, about 4,000 feet above sea level on Dove Mountain. Players could hear a thin coat of ice crunch under their feet as they walked onto the range.
In a duel between match play champions, Ogilvy warmed up quickly.
He captured the Accenture Match Play Championship a year ago at La Costa, going extra holes in his first four matches before coasting in the last two. Casey won the HSBC World Match Play Championship in England last September, steamrolling past an All-Star cast of challengers at Wentworth.
They exchanged birdies early, then Casey began to struggle.
He hit one tee shot so far left into the desert that Casey had to climb over a locked cattle gate of iron and barbed wire to reach his ball. Two holes later, he took an unplayable lie from under a desert bush, and he was three holes down at the turn. Ogilvy poured it on with three straight birdies, and he was the only player who still hasn't seen the 18th hole.
The Americans had a record-low 23 players in the 64-man field, and they had at least three quarterfinalists every year since the tournament began in 1999 until this year, when Campbell was left to carry the flag.
He did well in a wild match against Ames, who experienced partisan cheering.
Only two holes were halved as Campbell built a 2-up led, but Ames won three straight holes starting at No. 9 to take the lead. Campbell squared the match with a par on the 13th, then took the lead for good with a putt from one pace off the green at No. 14.
Walking off the 18th tee, a man shouted to Ames, "U-S-A! U-S-A!," and Ames turned and smiled. "Now I know what the Ryder Cup must be like," said Ames, who was born in Trinidad & Tobago and has citizenship in Canada.
Ames missed an 8-foot birdie putt on the 18th hole, leaving two Australians, an American and a Swede in the semifinals.