Spaniard Rahm made two late birdies to close with a two-under 69 for a two-shot win over home favourite Homa, finishing at 17-under for his 10th PGA Tour title and a fifth win in his last nine tournaments worldwide.
Homa, who won the 2021 title, shot a three-under 68 for a 15-under par total of 269, one stroke ahead of Patrick Cantlay.
Rahm's latest success was enough to overtake Scottie Scheffler, who was nine shots adrift, at the top of the rankings, only a week after the Masters champion had overtaken Rory McIlroy by defending his Phoenix Open title.
"I don't need a ranking to validate anything," said Rahm, who was last ranked at number one in March 2022. "I'm having the best season of my life, and hopefully I can keep it going.
"That was a tough week and a tough Sunday. To reach a milestone of double-digit wins is pretty incredible, and to do it at a golf course with this legacy, this history and hosted by the man himself, Tiger Woods, is a true honour."
Woods was in the spotlight as he returned to competition for the first time since last July's British Open and carded a final-round two-over-par 73 to finish on one under.
The 15-times major champion finished a 72-hole event for the first time since the Masters last April.
"My streak continues here," said Woods, who has played at the Riviera course 12 times without winning.
"It's progress, it's headed in the right direction. It was certainly a little bit more difficult than I probably let on."
