McIlroy, the top player in the Gary Player bracket, defeated his Ryder Cup teammate Miguel Angel Jimenez, 3 & 1, at the Ritz Carlton Golf Club. Sang-Moon Bae, the 11th-seed, beat John Senden, 1-up, in the other match-up in the Player bracket.
Westwood, the No. 1 seed in the Sam Snead bracket, bested No. 4 Nick Watney, 3 & 2. In the bottom half of that bracket, No. 10 Martin Laird won the battle of Scots with a 3 & 1 victory over Paul Lawrie.
The Bobby Jones bracket, where overall No. 1 seed and last year's winner Luke Donald was knocked out on Wednesday, features some long-shots.
McIlroy, who can become the No. 1 player in the world with a victory, built a 3-up lead over Jimenez at the turn Friday, but the Spaniard won 11 to go 2- down.
McIlroy claimed 12 with a bogey, but Jimenez answered with a birdie and a win at 13. That was the closest Jimenez got and when McIlroy hit it close at 17, Jimenez conceded the hole and the match.
"In parts, I played really, really well," McIlroy said in a televised interview. "Felt like I hit some really good shots on the front nine. Hit a couple of loose ones around the turn. Apart from that, I felt like it was really good."
Bae won the 16th when Senden made a mess of the hole, then had a chance to win the match at 17, but his five-foot birdie try lipped out of the hole. Bae, playing in his first WGC event, converted a four-foot par putt at the last to advance.
Westwood, who could also ascend to the top ranking in the world with a win, was in command out of the gate with birdies and victories at the first two holes. Watney got one back at three, but the Englishman amassed a 3-up lead at the turn.
Westwood won the 14th, and despite a Watney birdie for the win at 12, the match ended on the 16th green.
This week has given Westwood some form of redemption.
He's never made it this far at this championship, and for the last two years, Westwood was shown the door by Watney.
"A lot of new flags for me out here this week," Westwood joked about the different pin positions as the week goes on. "I'm fairly confident with the way I'm playing."
He will take on Laird, who grabbed victories at the first two holes. Laird never fell behind the 1999 British Open champion and took the match when Lawrie couldn't convert a 15-footer for par at the 17th.
Kaymer built the first lead of the match with a birdie at two, but when Kuchar was conceded the victory at four, they were all-square. Kuchar captured two more holes on the front nine to build his lead.
Kuchar won 10 and 11 with birdies to move 4-up. A bogey at the 12th cost him a hole, but he got it back with a birdie at 13 to once again go 4-up. The two halved the next two holes and the match went to Kuchar.
He will face Mahan, who never trailed against Stricker. Mahan won two and three and was 3-up by the turn. Stricker saw a flicker of hope with a win at No. 9, but Mahan took the next three holes to go 5-up with six to play.
Stricker got one back with a six-foot eagle at the par-five 13th, but the two halved the next two and Mahan earned his place in Saturday's quarterfinals.
Hanson, a member of the victorious 2010 European Ryder Cup team, never gave Snedeker much of a chance on Friday. Hanson swiped the first three holes, then won the sixth to go 4-up through six.
Snedeker clawed back with victories at eight, nine and 10, but Hanson won four of the next five holes, including a concession at 15, which proved to be the decisive hole.
Hanson will face Wilson on Saturday after Wilson once again took out Johnson. Wilson beat Johnson in 19 holes in last year's first round, but on Friday, Wilson played brilliantly on the front side.
Wilson, who won this year's Humana Challenge, hits it much shorter than Johnson, but Wilson won four in a row from the third to set the tempo. Wilson bogeyed the ninth, but Johnson made a mess of 10 and conceded the hole.
Johnson snuck in another win at the 11th, but Wilson birdied 12 to reclaim his 4-up cushion. The two halved the next three and Wilson is into the quarterfinals.
NOTES: The quarterfinals are on tap for Saturday, while the semifinals are scheduled for Sunday morning, with the final and consolation match in the afternoon.