Perry finished his four rounds in 19-under 261 at Fox Chapel, two shots ahead of Couples and Duffy Waldorf.
Perry was runner-up in the 1996 PGA Championship and 2009 Masters while playing as a regular on the PGA Tour. He tied for second in the Senior PGA Championship last month.
On Sunday, the 52-year-old Kentuckian hit close to the pin on Nos. 16 and 17 for tap-in birdies to break free from Couples and Waldorf. Couples began the day with a two-shot lead but missed a handful of short putts, opening the door for Perry.
Perry trailed by as many as eight shots in the second round before tracking down Couples over the weekend. He drew within two thanks to a pair of 7-under 63s in the second and third rounds. He followed with a nearly flawless round. Perry put together six birdies against no bogeys and shook loose late with a pair of superb irons.
Couples three-putted from 8 feet on the par-4 15th to put Perry in front by one. Perry followed by knocking his second shot to within 2 feet on the par-4 16th then did the same at the 231-yard par-3 17th to take a two-shot lead to the 18th tee. Couples had one last chance on the par-5, knocking it on in two. His eagle attempt from 45 feet stayed out to the right, ensuring a frustrating fourth second-place finish on the year.
It's a spot Perry has known all too well in the biggest tournaments. A 14-time winner during a lucrative PGA Tour career, Perry's sparkling record also includes a couple of high-profile collapses.
He held a one-shot lead over Mark Brooks at the 1996 PGA Tournament at Valhalla just outside Louisville, about two hours north of Perry's hometown of Franklin, Ky., only to bogey the final hole to fall into a playoff with Mark Brooks. Brooks birdied the first extra hole for the victory.
The heartbreak grew exponentially 13 years later, when he stood on the 17th tee at Augusta with a two-shot lead. Consecutive bogeys dropped Perry into a three-way tie with Angel Cabrera and Chad Campbell. He failed to get up and down on No. 10, the second playoff hole, and Cabrera made par to capture the green jacket.
Perry had another close call at the Senior PGA in May. He led through three rounds at Bellerive in St. Louis but was dogged by knee pain and overtaken by unheralded Kohki Idoki.
This time, there would be no folding.
Buoyed by a hot putter, Perry teamed with Waldorf to wear down Couples.
Waldorf began the day four strokes behind Couples but wasted little time making up ground. He rattled off four straight birdies to start the day, including tap-ins at 199-yard par-3 third and another at the 485-yard fourth. He and Perry forged a three-way tie with Couples when both players scrambled for birdie at the shot par-4 seventh while Couples three-putted for par.
Couples' problems worsened a few minutes later. On the par-4 eighth, his ball bounced off a sprinkler head behind the green and bounded 20 yards down the hill. He couldn't get up and down while Perry and Waldorf parred, dropping Couples out of the lead for the first time since he sprinted past John Huston early in the second round.
Waldorf briefly moved to the top of the leaderboard by himself after a short birdie putt on the ninth completed a sparkling 29 on the front. The fun, however, was just beginning as the three players spent the final nine holes jockeying for position.
Waldorf's pace finally slowed with a bogey on the 12th and another on the 15th. Couples and Perry each hit within 8 feet on the 15th. Both players missed their birdie putts, but Couples pulled his comebacker to the left. The Hall of Famer leads the Champions Tour in putting average but struggled on the greens on the final day.
Michael Allen and first-round leader John Huston tied for fourth at 12 under. Colin Montgomerie, playing in his first Champions Tour event, closed with a 65 to tie for ninth.