Mayfair, who is playing this year on his exemption for being on the top-50 on the PGA Tour career money list, shot a 5-under 67. He is at 14-under-par 130.
Calcavecchia opened his second round on the back nine and wasted little time in breaking into red figures. He two-putted from 65 feet for birdie at the par-5 10th, then added his second birdie at the next par-5. At 15, Calcavecchia could not reach the green with his second, but hit his third to 5 feet to set up birdie.
Calcavecchia knocked a pitching wedge to 5 feet for his second birdie in a row at 16. He parred his remaining holes to make the turn at 3-under-par 33.
It was once again a par-5 that moved Calcavecchia up the leaderboard. At the second, he two-putted from 30 feet for his fourth birdie of the round. He tallied another birdie at the fifth when he drained a 23-footer to get within one of Mayfair, who was in the clubhouse at minus-14.
Calcavecchia drove through the fairway at the par-5 eighth, then hit a 3-iron to the middle of the green. He ran home the 37-foot eagle putt to vault past Mayfair into first.
'After getting off to a good start yesterday, I knew I was going to make some birdies,' admitted Calcavecchia. 'Oddly enough, I tried to play smart, which I don't always do. I used my head today and stayed patient. My goal was to do something like that.'
Calcavecchia's strength this week has been his play on the par-5s. The 40-year-old is 8 under par on the longer holes so far and knows their importance.
'Three of them are reachable by pretty much everybody, so you need to birdie the par-fives for sure,' said Calcavecchia, an 11-time winner on the PGA Tour. 'It's just an enjoyable course in that sense. It's not hard. It's pretty defenseless.'
Mayfair played the course from the first and birdied No. 2 when he two-putted from 15 feet. He collected his second birdie in four holes at the fifth when he rolled in a 6-footer from over the flag.
Mayfair got it going again on the back nine. He missed the short grass at the par-5 10th, but hit a cut 4-iron into a greenside bunker. Mayfair blasted out to a foot for the tap-in birdie. He tallied his second in a row at 11 when his lob wedge approach spun back to 5 feet.
At the 13th, Mayfair hit a pitching wedge to 6 feet and converted the birdie putt. He parred out to put himself in position for his first tour win since the 1998 Buick Open.
'I was really happy with the way I played,' said Mayfair, who has yet to post a bogey this week. 'I gave myself a lot of birdie chances. If I could continue to do that, we'll see what happens.'
This tournament is opposite the WGC-Accenture Match Play Championship, but two former winners of that event crept into contention here. Kevin Sutherland (63) and Steve Stricker (68) were joined in sixth place by Doug Barron (66), Esteban Toledo (67) and Joe Ogilvie (66). That group is knotted at 12-under- par 132.
Mario Tiziani, who shared the opening-round lead with Mayfair, managed an even-par 72 on Friday and is tied for 18th place at minus-9.
The 36-hole cut fell at 5-under-par 139, a tournament record, and 70 players advanced to the weekend. Last year's winner Heath Slocum was not one of them as he finished two rounds at 1-under-par 143.