Rahm fired a bogey-free 67 on Sunday to get to 22 under, a total matched by American Landry who had a single blemish in his closing 68, birdieing the last to force the playoff.
"It's hard to believe to be honest, passing Jordan Spieth", he said.
"I know that I wouldn't have wanted to play the Stadium today", Cook said.
In addition to his P750 irons, Rahm added a P790 3-iron to the bag in place of his 5 wood, a change he made just this week for the tournament.
As for Rahm, he will defend his title next week at Torrey Pines riding a hot streak.
Though still in the hazard, his ball was playable nearly up against a rock but affording him a short backswing and while the recovery attempt was not without risk - another player had attempted a similar shot only to get into further trouble - Rahm chipped his ball out and two putted for bogey. He opened with a triple bogey and had six bogeys - four in a row to start his second nine - and only one birdie.
"I'm really proud of the way I played", Rahm said. "I felt like it was hard for those balls to break and I read it perfectly the first time and the next two times we had the exact same yardage, exact same putt right there, so just hit it a little too firm and tried to take some of the break out and it actually just kind of stayed high".More news: Britain's Kyle Edmund reaches quarter-finals of Australian Open
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"I feel super-rested and really in peace with my game and I think it shows", said.
"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", said Landry, who has three top-10s this season. They missed long birdie tries on the third extra hole, the par-4 10th.
After making an eagle and 11 birdies on the par 5s the first three days, Rahm settled for four pars in the final round, with the Pete Dye-designed layout playing tougher with many pin positions on the edges of greens. "One of us had to do it and either one of us would've been a well deserved champion".
"The course is firming up", Rahm said. "But there's a couple birdie putts, like the one on 14, that, if I'm being quite honest, I did not hit the line I wanted and it still went in dead center". "Kapalua wasn't the best ball-striking week of my life, but I was able to scramble really well and keep calm and have a good score".
Despite his impressive ball-striking, Rahm missed opportunities to give himself more of a cushion.
"Besides that, try to keep things going, try to keep playing good and hopefully do a better year than I did last year". Martin Piller, John Huh and Adam Hadwin each finished at 20-under. After kicking off in 63-70-64, the World No. 118 began with a one-shot lead over two players.