Westwood erased an early deficit to beat Martin Laird, 3 and 2. McIlroy never trailed in beating Bae Sang-moon by the same margin Saturday.
They play each other in the semifinals Sunday morning, each with a shot at No. 1 in the world if they go on to win this World Golf Championship.
Hunter Mahan played the shortest quarterfinal match in the 14-year history of this event in beating Matt Kuchar, 6 and 5. He will play MarkWilson, who had an easy time in his 4-and-3 win over Peter Hanson. That guarantees an American in the championship match for the first time since 2008.