Mark Calcavecchia, Michael Allen, Lucas Glover, Darron Stiles and Steve Stricker share third place at 8-under-par 64 at Omni Tucson National Golf Resort and Spa.
Mayfair flew out of the gate on Thursday. He started on the par-5 10th hole and knocked a 4-iron from 195 yards to 10 feet. Mayfair sank the eagle putt and kept the strong play going on the back nine.
He hit a lob-wedge to 4 feet to set up birdie at the 13th. Mayfair used a 3-wood off the tee at 14 and hit a sandwedge to 6 feet. He rolled that birdie putt in and capped off three in a row with an 8-foot birdie putt after missing the green with his second at the par-5 hole.
'I had things going my way,' said Mayfair, referring to his start on Thursday. 'I was real happy to just keep the momentum going all day.'
Mayfair wasted little time in breaking into red figures on his second nine. He hit a pitching wedge to 15 feet for birdie at the first, then made it back-to-back birdies with a tap-in at the par-5 second.
Mayfair polished off three birdies in a row at the third when his approach went slightly over the green. He hit a flop shot for his third and watched the ball roll into the center of the cup for birdie.
The 38-year-old, five-time winner on the PGA Tour had one birdie left in his round on Thursday. He drove into the right rough at the par-5 eighth, then missed his approach right of the green. Mayfair chipped to two feet and converted the short birdie putt to grab a piece of the first-round lead.
Mayfair is playing this year on his exemption for being on the top-50 on the PGA Tour career money list. He is hoping for some strong finishes this season to earn his privileges again.
'I would love to save it, but I was 48th and another bad year and I would have dropped out of the top-50,' said Mayfair. 'Maybe it was a wake-up call for me. It was a good time to use it.'
Tiziani, who toiled on the Canadian Tour for several years, also opened on the back nine and two-putted from 25 feet for birdie at the 10th. He added a tap-in birdie at the 12th to kick start a spectacular run of birdies.
At the 13th, Tiziani hit a pitching wedge to 3 feet to set up birdie. He used the same club at the 14th and ran home a 12-footer for birdie. Tiziani collected his fourth consecutive birdie at No. 15 with a 3-footer.
Tiziani's only bogey came at 17 when he three-putted from 15 feet. He returned to his birdie ways at two, then picked up his second in a row with a 12-foot putt at the third. He collected back-to-back birdies at five and six and closed his round with a 5-foot birdie putt at the eighth.
'I hit a lot of greens and gave myself a lot of chances,' said Tiziani. 'That's the key out here. Give yourself chances. Mine were closer than 10 feet.'