Phil Mickelson survived a triple-bogey 7 on his 14th hole in an otherwise excellent round to finish at 2-under 69, four strokes off the lead.
Fowler nailed some putts early then rolled in a long putt from the back of the green at the par-5 15th hole, his sixth, for an eagle.
"I know the back of the green there pretty well, know it's pretty straight and hit my line perfect."
He hit a 13-footer for a birdie at the par-4 9th to close his round.
After missing the cut last week at Torrey Pines, "I made a little bit of redemption" on Thursday, Fowler said. "But I know I have been swinging well and playing well. I just didn't make anything last week."
Lowry, who started on the back nine, shot a 5-under 31 in his first nine holes, including a 30-foot birdie putt before the packed stadium on the 16th hole.
Playing in his first Phoenix Open, Lowry found the set-up at 16 "very intimidating."
"I was just praying I was going to hit the green. My ball managed to just stay on the green and I rolled it in. It was pretty exciting."
Matsuyama had eight birdies and two bogeys to also complete his round in 65 just before play was suspended because of darkness; frost delayed the round's start by about an hour.
Matsuyama must like the TPC Scottsdale. He's tied for second and tied for fourth in his two previous appearances.
"I wish I knew (why), but I really enjoy playing here," he said through an interpreter.
Anirban Lahiri of India was second with a 5-under 66. Bryce Molder was 5-under through 16 holes when play was suspended.
Defending champion Brooks Koepka shot a 4-under 67, as did Brandt Snedeker, who was coming off his win Monday at Torrey Pines.
Bubba Watson and Kyle Stanley, the 2012 Phoenix Open champ, were among those who shot 2-under 69.
Mickelson, who -- like Fowler -- failed to make the cut last week, said he was encouraged with his round.
"I hit a lot of really good shots today, a lot of good iron shots," said Mickelson, who made his 27th start at the tournament (he is a three-time winner). "I probably didn't score as low as I thought I played, but I'm very encouraged with the number of quality shots I hit and how my game feels."
Mickelson, who started on the back nine, took an early lead by shooting a 5-under 31 on his first nine holes. But he bogeyed the par-3 fourth, then hit his tee shot way right and out of bounds on par-4 5th and finished with a 7.
"I hit a bad shot at the wrong time. It's the tightest hole out there. You miss the fairway five yards left, you're in the wash. You miss it right of the bunker, you're out of bounds.
"I just hit the one bad shot at the wrong time. But I'm not going to dwell on the one bad one because there were really a lot of good ones."
NOTES: Keegan Bradley was penalized two strokes for having one too many clubs in his bag at the start of the round. ... Attendance was listed at 101,021 at the world's most highly attended tournament. That's down significantly from last year's Thursday record of 118,461; Tiger Woods was among the competitors last year. ... The featured trio of Phil Mickelson, Zach Johnson and Jason Dufner will tee off on hole 1 at 12:16 p.m. Friday, MST. Fowler will tee off on hole 1 at 12:07 p.m. ...Fowler said he likes the sometimes-raucous atmosphere, noting, "I grew up around action sports, and this kinds of reminds me of being at action sports events, the fans being loud and having fun."... Lowry, who will be in the group that follows Mickelson on Friday, figures he'll hit No. 16 about 4:30 p.m. "I'm actually really looking forward to playing there. I'm pretty sure it's going to be fairly loud."... Mickelson on the changes made to the course before last year's tournament: "It's certainly longer and harder," with fewer birdie and eagle chances. "But it just means the scores won't be as low." Watson had criticized the course changes on Wednesday. ... Erik Compton withdrew during the second round; no reason was given.