All three golfers were tied for the lead entering No. 18. Triplett parred the last hole, wrapping up a round of 6-under 66 to finish at 16-under 200.
Langer (67) and Waldorf (66) each stumbled down the stretch at the TwinEagles Club, handing Triplett his third career win on the Champions Tour.
Also claiming a share of second place at minus-15 was Olin Browne (66).
Sole possession of fifth place went to Jay Haas (64) at 12-under 204.
Michael Allen (67) and Colin Montgomery (69) knotted for sixth at minus-10.