He set an Olympic record for 72 holes at 19-under 265. Great Britain's Tommy Fleetwood, who fell out of the lead with a bogey from the rough on the 17th, got up-and-down for par on the final hole for a 66 to win the silver medal.
Scheffler was visibly emotional during the medal ceremony as the national anthem played, appearing to wipe away tears in his eyes.
"I'm not big on comparisons or anything like that," Scheffler said when asked by NBC Olympics where this ranks among his accomplishments. "I'm just going to enjoy this moment. Like I said, I take tremendous pride in representing my country and I'm very proud to be going home, to be going back to the USA with a medal."
Hideki Matsuyama (-17) won the bronze. France's Victor Perez (-16) finished fourth, just off the podium. Ireland's Rory McIlroy (-15) and Spain's John Rahm (-15) finished tied for fifth.
USA's Xander Schauffele, who won the gold in the 2020 Tokyo Olympics, finished tied for ninth at -12. Wyndham Clark (-11) tied for 14th and Colin Morikawa (-5) finished tied at 24th.
