Langer shot a 7-under 63 on Desert Mountain's Cochise Course to take a two-stroke lead.
''I felt tremendous peace today, I really did,'' the 58-year-old German star said. ''That's when I play my best, when I'm not bothered by anything, I'm just walking along enjoying the scenery and having a blast playing golf and doing it well.''
Langer began the week third in the Charles Schwab Cup race, 66 points behind Montgomerie and 27 behind Maggert. With players receiving a point for every $500 earned in the $2.5 million tournament, Langer was $33,000 behind Montgomerie and $13,500 behind Maggert.
Montgomerie had a 70, leaving him tied for 17th in the 30-man field. Maggert three-putted the par-5 18th for a bogey and a 72 that dropped him into a tie for 24th.
Langer is trying to win the season title for the second straight year and record third time overall. The champion will receive a $1 million annuity, the runner-up a $500,000 annuity, and the third-place finisher a $300,000 annuity.
''I'm going to keep an eye on it, but the key is I've got to play my own golf,'' Langer said. ''I've got to play my game and that was my mindset going into the tournament. I've got to play the best I can and if I do really well, then I might end up in front of them, and if somebody else is better than me, so be it. It's not life and death.''
''It was a great way to start,'' Andrade said. ''Haven't started a tournament like that with a hole-in-one before, so, of course, you automatically bogey the next hole.''
Langer played the front nine in 5-under 30, birdieing Nos. 2 and 5-8, and added birdies on Nos. 12 and 13. He hit 5-irons to a foot on the second and 6 inches on the fifth.
''Got off to a really nice start, hit most of my targets, hit fairways, hit greens and hit it pretty close,'' Langer said. ''Then started to putt nicely, too.''
The two-time Masters champion had only 24 putts. He made a 12-foot par save on the par-4 16th after hitting into the left greenside bunker, and got up and down from the right bunker on the par-3 17th.
The tournament is Langer's last before the Jan. 1 ban on the anchored putting stroke that he has used with a long putter for 17 years.
''I've thought about it a little bit,'' Langer said. ''I've gathered a few putters, different styles, different lengths, different grips. My first thought is I'll probably go back to what I did before I went to the long putter, which was what [Matt] Kuchar does, holding the putter against the left forearm that way, and Soren Kjeldsen in Europe does the same thing. I putted that way for seven years and I won a number of tournaments including the Masters, and if you can putt on the Masters greens and win with a grip like that, I would think I could do it in other tournaments, but we'll see. There's other options.''