Maggert birdied three of the first four holes in a front-nine 31 and capped the bogey-free round with a birdie on the par-4 17th in perfect conditions at Phoenix Country Club. He had a 14-under 128 total.
"A good start again. I hit the ball very well on the front nine," Maggert said. "Not so much on the back nine, but had a lot of good par saves. Didn't leave myself with a lot of pressure putts today. I made a nice 10-footer for par on, I think, No. 11. Other than that, my up-and-downs, I was chipping it pretty close. And got lucky on 17 and holed a bunker shot."
The 55-year-old Texan entered the season-ending event 31st in the Charles Schwab Cup standings, just three spots from failing to qualify. He won three times on the PGA Tour and has five senior victories, one in 2014 and four in 2015.
"I haven't played well this year and I wanted to finish the year off on a good note," Maggert said. "But we're only halfway done. I need to play a lot more good golf over the next two days. ... Looking forward to just keeping the foot on the gas pedal and trying to make birdies over the weekend."
Langer closed with a double bogey after hitting into the water on the par-5 18th. Coming off a playoff loss to Colin Montgomerie on Sunday in California, Langer is third in the standings behind Scott McCarron and Jerry Kelly.
"I hit my bunker shot fat," Langer said. "I was hoping to get a lot closer with the sand wedge. And I was caught between a 9-iron and a wedge, and used the 9-iron and pushed it." To take the season title, the 62-year-old German star needs to win the event and have McCarron finish in a two-way tie for fifth or worse and Kelly finish in a two-way tie for second or worse. McCarron (71) and Kelly (74) were tied for 25th at 2 under.
"I'm putting well, which is key," Langer said. "I'm not quite totally happy with my ball-striking, but if I get my ball-striking sorted out, I feel I can really put a charge on, because my short game is good."
Retief Goosen, fifth in the standings, had his second straight 67 to join Brandt Jobe (66) and Marco Dawson (67) at 8 under. Miguel Angel Jimenez (70) was another stroke back with Joe Durant (66), Wes Short Jr. (67) and Steve Flesch (70).