Former champion Ian Poulter admitted he got what he deserved after suffering his third first-round exit in four years from the WGC-Accenture Match Play Championship on Wednesday.
But Graeme McDowell joined Ryder Cup team-mates Rory McIlroy, Sergio Garcia and Peter Hanson in the last 32 at Dove Mountain thanks to an unlikely comeback against Gary Woodland.
McDowell was four down after seven holes and still three down with three to play but won the 16th with a par, the 17th with a birdie and was conceded the 18th when Woodland went from one greenside bunker to another.
A birdie on the first extra hole then sealed victory over a shellshocked Woodland, with whom he had shared a private jet from Florida to Arizona.
"I missed a short one on 15 to follow him in for birdie and he looked unbeatable," McDowell admitted. "He hit a six iron all over the flag on the 16th and I thought my manager had a plane ticket booked for me and I was going home.
"I feel very fortunate to have got through that match. Gary is a good friend and a great player and I think he's one to watch this year."
Former champion Poulter had earlier lost 2&1 to American Rickie Fowler, who led from the fourth hole onwards and will now face compatriot Jimmy Walker in the second round. Walker, who has already won three times in the 2014 PGA Tour season, secured the first victory of the day with a comfortable 5&4 win over South African Branden Grace.
"Disappointed with my performance today, did not deserve to move on," Poulter wrote on Twitter. "Congrats to Rickie Fowler."
McIlroy lost to Shane Lowry in the first round 12 months ago but had a comfortable 3&2 win over Boo Weekley this time around to set up a last-32 clash with Harris English, who beat former world number one Lee Westwood 5&3. Another former number one, compatriot Luke Donald, also made an early exit as he was thrashed 5&4 by Matteo Manassero.
"I played well I guess for the first 12 holes," said McIlroy, whose wayward second shot on the 15th had spectators ducking for cover and saw one unfortunate man covered in cactus stems known as 'Jumping Cholla'.
"I might have got a bit complacent the last few holes and gave Boo a couple but I'm just happy to get through to the next round."
A total of four matches so far had gone to extra holes, Garcia needing 22 holes to get past Marc Leishman, Brandt Snedeker beating David Lynn on the 20th and Jason Dufner edging past Scott Stallings on the 19th.
Finland's Mikko Ilonen had looked like creating a shock when he led the in-form Bubba Watson by two holes with six to play, but lost the next three and Watson - who claimed his first win since the 2012 Masters in the Northern Trust Open on Sunday - sealed a 2&1 win on the 17th.
Defending champion Matt Kuchar also advanced to the second round, but only after having to win his match with Austria's Bernd Wiesberger twice.
Kuchar thought he had sealed a 5&4 win on the 14th, only to realise he had failed to move his ball marker back to its correct position before holing a birdie putt. That cost him the hole and meant the match continued, but the world number 10 still had a three-hole cushion and eventually won 3&2.
"It's an interesting lesson learned," Kuchar told Sky Sports. "I had about a 16ft putt and Bernd had about 20ft on exactly the same line so he asked me to move my mark, which I did, and I just got so involved with watching his putt and then having a chance to win the match that I completely forgot.
"It was my bad, something that has never happened to me before. I made the putt and shook hands and then there were a few questions as to whether I moved it and I knew right away I hadn't so we had to continue on."
Elsewhere, Hanson beat Dustin Johnson 4&3 - the world number eight's fifth first-round loss in six years - to set up a meeting with France's Victor Dubuisson, who saw off Kevin Streelman 5&4.
Sweden's Jonas Blixt enjoyed a 2&1 win over former US PGA champion Keegan Bradley and South African George Coetzee saw off Steve Stricker 3&1. Stricker's participation in the event had been in serious doubt until his brother underwent a successful liver transplant at the weekend.
The biggest margin of victory belonged to American Billy Horschel, who thrashed Welshman Jamie Donaldson 6&5, while Bill Haas beat Miguel Angel Jimenez 5&4 and Thomas Bjorn defeated Francesco Molinari 2&1.
Top seed Henrik Stenson had to come from behind to eventually beat Kiradech Aphibarnrat 2&1, while US Open champion Justin Rose was taken to the 18th before edging past Scott Piercy.
That left one match on the course and Ernie Els won the 16th and 17th with pars to get back on level terms with Scotland's Stephen Gallacher.
Gallacher looked like securing victory following a superb approach to the last after Els found a bunker with his approach, but Els splashed out to two feet and Gallacher missed from five to send the contest into extra holes.