On another breezy day of dazzling sunshine in Arizona's high desert, Fowler came from one down with three holes to play, sealing his second win of the week with a birdie on 16 followed by well executed par saves on 17 and 18.
"I told my caddie, Joe, let's try and birdie the last three, make some good swings," Fowler told reporters. "I didn't birdie 17 and 18, but I made two really good putts along with the birdie putt on 16."
Fowler, who upset matchplay expert and 2010 champion Ian Poulter in the opening round, was delighted to add the scalp of Walker, who has already won three times on the 2013-14 PGA Tour.
"Jimmy, he's arguably the best player the last six months or so with three wins," said Fowler. "He's on top of his game. I knew coming in today that even if he didn't bring his 'A' game, he was going to be tough to beat.
"We had a fun match. Definitely nice to come out on top."
TOOK CONTROL
Garcia, who had battled past Australian Marc Leishman after 22 holes in his opening match, was two down after seven holes but sparked his fightback with an eagle at the eighth before taking control with three birdies after the turn.
"Very pleased," said Garcia, who will take on Fowler in the third round. "Good friend of mine (Haas). I thought he played really, really well early on.
"Then I was able to go on a very nice run from the eighth hole onwards, put on a little bit of pressure and very pleased with just playing 17 (holes) today."
American Jordan Spieth, the 2013 PGA Tour rookie of the year, was always in command against Denmark's Thomas Bjorn before wrapping up a comfortable 5&4 victory.
Frenchman Victor Dubuisson, a debutant at Dove Mountain this week, never trailed on the way to a 3&1 win against Swede Peter Hanson.
Dubuisson will next face former Masters champion Bubba Watson, who beat Swede Jonas Blixt two up.
In other matches, top-seed Henrik Stenson of Sweden was two down to South African Louis Oosthuizen after 10 holes while fourth-seeded Northern Irishman Rory McIlroy trailed American Harris English by one after 14.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine)
