Westwood's 7-under round pulled him into a tie for fifth with Bo Van Pelt at 11-under. Haas and Harrington are in a group at 9-under.
McIlroy, coming off a win at last week's Deutsche Bank Championship, and Woods were paired together for Thursday and Friday. McIlroy, who had one bogey Thursday, fought through a round Friday that included four bogeys while Woods charged in with three birdies in his final four holes.
They each had birdies on the final hole to keep within one of Singh.
Singh had four consecutive birdies in a middle stretch of his second round to grab the lead.