Northern Ireland’s McIlroy, who earned his second career major title at the PGA Championship in August, had a 12-under total of 130 after two rounds on the par-71 TPC Boston layout.
South Africa’s Oosthuizen, the 2010 British Open champion, was one shot back after a 65 for 131 and 14-time major champion Woods carded a 68 for 132, where he was joined by compatriot Ryan Moore, who also carded a 68.
McIlroy’s round included an eagle on the revamped par-five 18th — his ninth hole of the day — where he stuck his approach shot eight feet from the pin.
He had two bogeys on his inward nine, finding the water at the par-five second for a six and also bogeying the par-three third. But he bounced back with birdies at four and five and was in the clubhouse on 12-under 130. Overnight leader Seung-Yul Noh of South Korea had an even par 71 that included an eagle and a double-bogey and was in a group of five players on 133 that also included South Africa’s Charl Schwartzel (65).