Making his first competitive appearance since 2006 at Riviera Country Club – he made his PGA Tour debut there as a 16-year-old – Woods carded a one-over-par 72.
One more than McIlroy’s effort, that started with a birdie at the 10th before a lost ball up a tree cost the 14-time major winner a double-bogey 7 at the next.
He then dropped to two-over with a bogey at the 12th – his third – but had four birdies thereafter in covering the remaining holes in one-under.
“It was a decent start,” said Woods, who is playing in just his second PGA Tour event since making his comeback from injury late last year, afterwards. “I made a lot of birdies but also some silly bogeys. Overall, it was pleasing to fight back to level from two-over, though I then finished one-over.
“The course is playing tough, it really is, and hopefully I can shoot a good number tomorrow afternoon and work my way up the leaderboard.”
Elsewhere, Marc Warren fared best out of a seven-strong Scottish contingent in the first round of the NBO Oman Open after Bradley Neil went from playing “near-perfect golf” to slipping down the leaderboard.
On a day when English duo Paul Waring and Matt Southgate carded matching seven-under-par 65s to share the lead in Muscat, Warren opened with a 69 to sit joint 12th in the historic event.
The 36-year-old made his score with a burst of three birdies in four holes at the start of his back nine at Al Mouj Golf, which is hosting Oman’s first European Tour event after staging the Challenge Tour Grand Final for the last three years.
Carding six birdies in total, Warren finished the day a shot ahead of compatriot Connor Syme and two in front of Paul Lawrie after they both compiled rounds containing four birdies. Lawrie’s effort came in his first outing with Damian Moore, who caddied for Stephen Gallacher when he won the Dubai Desert Classic two years running, on the bag.
On his return after missing two scheduled events due to back trouble, David Drysdale signed for a 72 while Neil and Stephen Gallacher both had to settle for 74s after poor finishes. Neil, who secured his European Tour card on this course last November, was out in 34, two-under, before moving to four-under with birdies at 12th and 13th.
However, that good work was undone as the 22-year-old then dropped six shots in four holes in a damaging run.
Gallacher was two-under with four to play before following a bogey at the 15th with a triple-bogey 8 at the 16th.