They took advantage of warmer and calmer afternoon conditions and held a one-stroke lead over a group of four players including three-time major winner Padraig Harrington at 4 under.
Harrington and Billy Horschel shared the lead following the morning tee times, battling chilly and windy conditions. They were joined by Bryce Molder and Harris English at 4 under in the afternoon.
McIlroy, who entered the tournament as a final opportunity to prep for next week's Masters, opened with an even-par 72 and is tied for 45th.
Playing partners Suzann Pettersen and Na Yeon Choi took advantage of perfect morning conditions to share the first-round lead with Jodi Ewart Shadoff in the Kraft Nabisco Championship.
Finishing before the temperature climbed into the low 90s on Thursday in the Coachella Valley, Pettersen and Choi had bogey-free rounds of 4-under 68 at Mission Hills.