Play will resume Saturday at 7:00 A.M. (ET).
'Well, I'm delighted,' said Peoples. 'I don't think I've ever put two 65s together to start a tournament out, so obviously I'm very happy about it.'
Conditions were benign on the Sunset Course at the Country Club at Mirasol and after the rain from the night before put lift, clean and place rules in effect, players were determined to go low.
Peoples, a veteran of the PGA Tour whose last victory came in 1992, was two shots off the pace to start the second round. He played the back nine first and dropped a 9-iron inside eight feet for a birdie at the 13th.
The 43-year-old chipped in for eagle at the par-5 15th but struggled with a bogey at the following hole. Peoples recovered at the par-5 17th, however, with a two-putt birdie to make the turn at 10-under.
Peoples rolled in a 12-foot putt from off the fringe at the par-5 fifth for the first of three consecutive birdies. At the par-5 ninth, his last, Peoples hit his third shot from off the green to five feet and drained the putt to take the lead at minus-14.
'The only thing that can change is the conditions. If the wind blows like it normally does in south Florida, that will change everything,' said the former Florida Gator. 'But if it stays the same, I think that you have to stay aggressive without being overly reckless.'
Begay, who struggled in 2002 with 11 missed cuts in a row to open the season, seems to have regained the form that saw him capture four PGA Tour titles since joining the tour.
He had a share of the lead after round one and jumped out of the gate Friday with a pair of birdies from the third.
Begay found trouble with a bogey at the sixth but recovered with a birdie at the eighth after his second shot landed within two feet of the cup.
The 30-year-old birdied the 10th but faltered with a bogey at the 14th. Begay countered with a birdie at the next to get to 12-under and reached the green in two at the par-5 17th. Begay ran home the eagle putt to join Peoples in first after a first-round 67.
'I had a great round,' said Begay. 'I made a couple bogeys today that I wasn't really happy with, but overall I'm very satisfied. It's been a long time and I knew that I've worked hard enough to get my health back and my game back.
'I'm not afraid to win. That's my objective. You either go out and try to win or you don't.'
Davis Love III, Tom Byrum and Esteban Toledo were tied for third at 13-under-par 131.
Tim Herron, Jerry Kelly and John Huston are two shots off the pace at 12-under-par 132. Jeff Brehaut, who held a share of the first-round lead, was at 12-under through 15 holes.
'It's important for me to come back every year to the Honda even if they change the venue and a venue that doesn't quite fit my game,' said Herron, who earned his first career victory on the PGA Tour at this event in 1996. 'It's kind of a sentimental thing.'
Defending champion Matt Kuchar posted a 5-under 67 to finish in a group at 7-under-par 137.