"Tough conditions out there, and I didn't exactly play my best, either," said Woods, who had his worst 36-hole total (145) at the Memorial since he first played it in 1997.
McIlroy was in danger of missing the cut until he fired off five birdies, looking more comfortable with his putts and attacking with his driver. He was 4 under for his round and one shot inside the cut line and one shot behind Woods. McIlroy was in a greenside bunker in two shots at the par-5 15th when play was stopped.
"The major goal today was to try to make it into the weekend," McIlroy said. "I'm on the right track to do that."
Three-time NCAA player of the year Amanda Blumenherst and LPGA rookie leader Moriya Jutanugarn shot 5-under 66 to top the leaderboard in the ShopRite LPGA Classic in Galloway Township, N.J., a stroke ahead of defending champion Stacy Lewis.
Tom Lehman, Duffy Waldorf, Dan Forsman and Scott Hoch shot 3-under 69 on Friday to share the first-round lead in the Champions Tour's Principal Charity Classic in Des Moines, Iowa.
Hale Irwin, who turns 68 on Monday, topped a group of eight at 70.
Bill Haas -9
Matt Kuchar -6
Robert Karlsson -4
Pat Perez -3
Hunter Mahan -3
Matt Jones -3
Tiger Woods +1
Note • Play suspended due to dangerous weather with 42 players on the course.