The 52-year-old went from 10 shots behind pacesetter Michael Allen at the halfway mark of the tournament to a five-stroke victory in Omaha, Nebraska.
Perry, a winner of 14 PGA Tour titles including a trio of trophies at the Memorial Tournament, said the victory at Omaha Country Club was the highlight of his career.
"Today's round was probably the greatest round I've ever played," said Perry, who had a 13-under-par total of 267.
"I just was spoton with all my irons. I putted like Ben Crenshaw. It all just came together for me. It's just been a remarkable month. I've had a great run."
Perry, who two weeks ago won the Senior Players Championship, shot a 64 in the third round and finished with a seven-under round on Sunday.
Fellow American Fred Funk, who shot a final-round 68 for eight-under-par 272, was in second place.
Another stroke back were Rocco Mediate (66) and Corey Pavin (67) on 273, with Allen a further shot behind after finishing with a two-over 72.
"He put it to us. Six-under yesterday and seven-under today. Backtoback, it's kind of what he did two weeks ago at Fox Chapel," said Funk. "He just smoked the field on the weekend. That's what you got to do. He just lapped us."
Perry erased the previous record for the biggest comeback after 36 holes in a senior major, which was seven strokes.
The Kentuckian also set a new standard for the lowest score over the final 36 holes of the U.S. Senior Open at 127, three better than the old mark, and tied records for lowest 72-hole total, lowest score for the last 54 holes (200), and the lowest final-round score.
For Perry, who came agonizingly close to winning a PGA Tour major, winning a national Open was the sweetest of victories.
"It means a lot to win a national Open. For me to have that now attached to my name, (it is) the greatest win I've ever had," he said.
"To lose a Masters in a playoff (2009) and lose a PGA Championship in a playoff (1996), heartbreak. All I felt was heartbreak.
"To finally get it all together and to finally have a major two majors - attached to my name, is very sweet."
Perry began the final round two shots behind Allen, but back-to-back birdies from the second hole set the tone for his brilliant finish.
After a bogey at the fifth, Perry made four birdies in a row to make the turn at five-under 30, needing only 10 putts as he took command of the championship.
In winning the U.S. Senior Open, Perry became the 11th player to win back-to-back senior majors.
(Reporting by Larry Fine in New York; Editing by Peter Rutherford)