Fowler, who missed the cut at Torrey Pines six day ago after winning the previous week at the European Tour's Abu Dhabi Championship, mixed an eagle at the par-five 15th with six birdies and two bogeys.
India's Anirban Lahiri carded a seven-birdie 66 and American Bryce Molder also got to five under with two holes to complete before play was suspended for the day in fading light with 33 players still on the course.
"I was just making putts finally," Fowler, 27, told Golf Channel about the biggest change in his game since his surprising missed cut at last week's Farmers Insurance Open outside San Diego.
"I couldn't get anything going the whole of last week and it's really tough to get a rhythm or any momentum to build up as the round goes on if nothing's going in.
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"So it was nice to see one go in on the first hole today and I continued to roll some in, got off to a great start and closed it off nicely," said Fowler, who sank a 16-footer on his opening hole and a 12-footer at the last.
Lowry, a double winner on the European Tour before he claimed his first PGA Tour victory at the elite WGC-Bridgestone Invitational last year, also owed much to improved putting.
"I holed some putts, maybe three or four putts outside 20 feet ... and I haven't done that for a while," said the 28-year-old, whose highlight came at the par-three 16th where he drained a 30-footer in front of a raucous stadium crowd.
"I've worked a lot on my putting the last couple of weeks and it paid off today. Hopefully it keeps paying off at the weekend."
Three-times former winner Phil Mickelson, a popular figure at Scottsdale after attending the nearby Arizona State University, made a storming start as he got to five under in eight holes before losing momentum after the turn to card a 69.
"I hit a lot of good iron shots today, so I'm encouraged that as the week wears on and the days come on, it's going to keep getting better and better," said the American left-hander.
"I've got a lot of good things that came from this round."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Steve Keating.)
