Two-time winner Fred Couples opened with a 5-under-par 66. He was joined in a tie for third place by 2000 runner-up Jesper Parnevik, 1998 winner Billy Mayfair and Bob Estes.
First-round play at Riviera Country Club was suspended with eight players remaining on the course. Those eight players will resume their opening rounds at 11:00 a.m. ET on Friday. The second round will start as scheduled at 10:00 a.m.
Woods was all over the place during his opening round. He birdied the first, but bogeyed the next. The 30-year-old then double-bogeyed the par-3 fourth after missing the green well left of the putting surface.
The reigning Masters and British Open champion managed to get those two strokes back with birdies on six and seven. Woods got into the red at minus-2 as he birdied the ninth and 10th.
Woods got to 3 under with a birdie on the par-5 17th. However, the world's No. 1 player bogeyed the last to end at minus-2. Woods is battling a cold that bothered him throughout the round.
'I am disgusted at how I'm hitting it,' Woods said. 'Wishing my head would clear up, wishing this fever would break. It's not going to happen. Considering everything, I will take 2 under in a heartbeat though. Anything under par is a great score the way I feel.'
Rose opened his round on the back nine at Riviera. He dropped in back-to-back birdies from the 11th. After parring his next three holes, Rose rolled in a birdie effort on the 16th to get to 3 under.
Around the turn, Rose birdied the par-5 first to move to minus-4. He kept climbing the leaderboard as he birdied the par-3 fourth.
The 25-year-old came back two holes later with another birdie. Rose birdied No. 8 to grab a share of the lead.
'I am obviously really happy to get off to a good start,' said Rose, who has won twice on the European Tour. 'It's always nice to feel like you get into the tournament from the word go. That's what happened today. I birdied my second and third holes. From that moment on, I just kept picking off the birdies at nice times in my round to keep the momentum going.'
Wilson also began on the second nine and he two-putted for birdie on his first hole to get off to a quick start. He collected his second birdie on the 13th, his fourth.
The 36-year-old caught fire around the turn. Wilson birdied the par-5 17th and came right back to birdie the 18th.
The Hawaiian picked up his third straight birdie on the first to get to minus-5. Wilson, who has won six times in Japan, dropped in consecutive birdies from the sixth to move to 7 under. He parred his final two holes to share the lead with Rose.
'I started on the back side, and I played really nice. I started off hitting a driver on the first hole, the 10th, and got it on the green and just two-putted from there,' Wilson said. 'So that got me off to a good start. My first nine holes, I just played really nice. I don't think I missed a fairway or a green. I had some good momentum to build on.'
Chad Campbell, who lost to Adam Scott in last year's playoff, opened with a 4-under 67. He was joined in a tie for seventh place by U.S. Ryder Cup captain Tom Lehman, Rod Pampling, Corey Pavin, Rory Sabbatini, Harrison Frazar and Trevor Immelman. Jason Schultz and Craig Barlow are also at minus-4, but have to complete the 18th hole.
Scott is one shot behind that group at minus-3.