Rahm and Landry each missed chances to win on the first two extra trips down 18. Rahm's 9-foot birdie try slid left on the first, and Landry's 8-footer went by to the right on the second. They missed long birdie tries on the third extra hole, the par-4 10th.
Rahm parred the four par 5s on Sunday, with the Pete Dye-designed layout playing tougher with many pin positions on the edges of greens, after going 13 under on 12 par 5s in the first three rounds with an eagle and 11 birdies.
"It's been a fighting day," Rahm said. "I've been a ball-striking clinic most of the week and in the playoff I was just not making the putts. I just got fortunate that none of us really made any and I was able to make the one that mattered. But then again, it was really supreme ball-striking on my part today. Especially, on the back nine, I hit the ball as good as I can."
Rahm started the week with a career-best 62 at La Quinta Country Club, shot 67 on Friday on the Nicklaus Course and had a 70 at the Stadium on Saturday.
The former Arizona State star was second behind Johnson two weeks ago at Kapalua in his first start since winning the European Tour's season-ending event in Dubai in November. Rahm will open his Torrey Pines title defense Thursday in San Diego.
The 30-year-old Landry had his best career PGA TOUR finish and third top-three finish of the season.
"I've been playing well all year, had a great season last year and I'm rolling it over right into this, into the fall and now starting the year out," Landry said. "Second-place finish, we'll take it and move on next week to Torrey Pines."
Adam Hadwin (68), Martin Piller (70) and John Huh (66) tied for third at 20 under, and Kevin Chappell (67) and Scott Piercy (70) were another stroke back.
Third-round leader Austin Cook had a 75 to tie for 14th at 16 under.
"Ball-striking just kind of disappeared today," Cook said.