Murray beat defending champion Novak Djokovic 7-6 (10), 7-5, 2-6, 3-6, 6-2 on Monday in his fifth try in the final of a major tournament.
The 25-year-old Scot was reeling going into the decisive set after Djokovic rallied from two sets down to even the match. But Murray broke the Serb's serve in the first game, then broke again to go up 3-0.
When it was finally over after a record 4 hours, 54 minutes full of long, scintillating rallies, Murray crouched to the court with both hands over his face.
Fred Perry won Britain's last Grand Slam men's title 76 years ago at the U.S. Championships, the Open's predecessor.