Langer was two strokes better than Lonnie Nielsen despite taking a one-stroke penalty on No. 3, when he absent-mindedly picked up his ball after driving to the green.
After a week of rain before the tournament, wet conditions at The Woodlands Country Club course had allowed for lift, clean and place the first two rounds but that courtesy had been lifted for the final day.
Nielsen had three birdies and a bogey on the front nine. He also bogeyed No. 10 and carded a 1-under 71 for the round.
Langer won last years Administaff by eight strokes when he finished 25 under.
He started the day in a three-way tie for the lead with Nielsen and Brad Bryant. Bryant triple-bogeyed 13, shot a 77 and finished 4 under, in a three-way tie for 20th.
Champion Tour points leader Fred Funk placed third, just three strokes back of Langer. Funk also shot a 3-under 69 in the final round.
Dave Stockton had four straight birdies on the back nine to finish with a 70 and in a tie with Denis Watson for fourth place at 8 under.
Hal Sutton, playing in his first Champions Tour event, carded a 72 to finish 3 under and tied for 23rd.