Langer appeared to be in trouble when his second shot on the par-5 18th ended up in the rough short of the green. He hit a brilliant pitch to 5 feet and made the putt after Sluman's birdie attempt rolled just wide.
The victory was the 56-year-old Langer's third of the year and his third major title on the Champions Tour. The two-time Masters champion shot an even-par 70 to finish at 15-under 265 at Fox Chapel.
Sluman had a bogey-free 65 to match Langer, but narrowly missed a birdie putt on the first playoff hole that would have won it.
Russ Cochran, who trailed by seven shots early in the final round, had a 67 to finish third at 14 under.
Defending champion Kenny Perry tied Langer for the lead heading into the back nine, but faded badly over the closing holes. Perry's 69 left him two shots out of the playoff.
Langer nearly missed out on the playoff himself. He fought a balky putter much of the day only to hole a 35-foot birdie putt on the 17th that lifted him into a tie with Sluman. The normally reserved German pumped his fist in disbelief after the ball dropped into the cup. He parred 18 to match Sluman at 15 under and escaped one more time when Sluman's birdie attempt on the first playoff hole burned the right edge.
Sluman, the 1988 PGA champion, covered his hands in disbelief after the putt stayed out. Langer didn't let the reprieve go to waste, birdieing the 18th on his third try to earn his first major title on the 50-and-over circuit since the 2010 Senior British Open.
It didn't come easy for a player who started the day with a comfortable three-shot advantage over Perry.
The steady play that kept Langer atop the leaderboard for the better part of 54 holes abandoned him early in the round, opening the door for the rest of the field. Langer missed a short par putt at the par-4 fourth, and he turned the 295-yard par-4 seventh into an adventure when his pitch sailed over the green and his 5-foot comebacker for par popped off the back edge of the cup.
Perry, who promised to go into ''attack mode'' to chase down his good friend, had little trouble tracking Langer down. He pulled even with a birdie at the seventh and did it again at the ninth, when he bounced back from a bogey at the eighth by holing out from a greenside bunker for birdie.
A back-nine duel, however, never materialized. Both players started spraying shots - including an ugly double bogey for Langer at the par-4 12th - while Sluman quietly went about his business in the group ahead.
Sluman slowly reeled in the front-runners, taking the lead with a birdie on the par-4 14th and adding another at the par-4 16th while Perry and Langer faltered behind him.
The streaky Perry, trying to join Arnold Palmer as the only player to win consecutive Senior Players titles, cooled as the pressure mounted. He shot 3-over 38 on the back, failing to make a single birdie down the stretch as the crisp iron game that vaulted him into contention vanished.