Westwood, who has led 48 of the 49 holes he has played this week, got a small measure of revenge against Nick Watney and advanced to the quarterfinals with a 3-and-2 victory on Friday at Dove Mountain. Watney had eliminated him each of the past two years.
McIlroy built a 3-up lead at the turn and hung on to beat Miguel Angel Jimenez, 2 and 1.
Westwood or McIlroy would go to No. 1 in the world with the title in this World Golf Championship. If they win their quarterfinal matches today, they would meet in the semifinals Sunday morning.
"It's a nice incentive," McIlroy said. "It's nice to have in the back of your mind. And if you're struggling in a match and find it hard to get yourself up, or get any sort of momentum, if you think about that and you think if you can really dig deep, you still have a chance to become No. 1."
Westwood was at No. 1 a year ago, and it's a less of a priority than to capture his first World Golf Championship.
One year after Luke Donald became the first Match Play champion to never trail all week – Donald never even played the 18th hole in his six matches – Westwood is looking every bit as dominant.
Westwood had never made it out of the second round in 11 previous trips to this fickle tournament.
"I'm just happy to be looking for a different restaurant for Friday night," Westwood said.
Westwood next plays Martin Laird, who took down former British Open champion Paul Lawrie, 3 and 1.
Next up for McIlroy is Bae Sang-moon, the surprise in his first Match Play Championship. Bae won three times last year on the Japan Golf Tour. And while he made it through Q-school to earn a PGA Tour card, he ended last year at No. 30 in the world He is no stranger in global golf, as McIlroy knows all too well.
They played in the final group of the Korea Open in 2009, where McIlroy and Kim Dae-sub were tied for the 54-hole lead. Bae closed with 67 and beat them both.
Bae had the only match that went 18 holes, beating John Senden.
In other matches:
• Hunter Mahan took advantage of some mental lapses by Steve Stricker to build a big lead and held on for a 4-and-3 win. Mahan will play Matt Kuchar, a 4-and-3 winner against Martin Kaymer.
• Mark Wilson overwhelmed Dustin Johnson for the second consecutive year. Wilson will play Peter Hanson who knocked off Brandt Snedeker.