Two months after making his major breakthrough in the US PGA Championship at Valhalla, Schauffele carded a bogey-free 65 on Sunday to finish nine under par, two shots ahead of Billy Horschel and Justin Rose.
"At the very tip-top, the best round I've played," Schauffele said on Sunday, when asked to rate his final round.
The Olympic champion began the day a shot behind Horschel but birdied the sixth and seventh in a front-nine of 34 and picked up further shots on the 11th, 13th, 14th and 16th to succeed compatriot Brian Harman as Open champion.
"It's an honour, I've always dreamt of doing it," the 30-year-old said.
"That walk up 18 truly is the coolest with the yellow leaderboards and the fans and the standing ovation. It really is one of the coolest feelings I've ever had in my life.
"I got chills walking down and quickly had to zap myself back into focus because the tournament wasn't over yet. I can't wait to enjoy this with my family."
Schauffele had previously suffered a reputation of being a player who struggled to close out big tournaments, but felt his victory at Valhalla in May stood him in good stead in South Ayrshire.
"It was hard. It was very difficult," he said. "I think winning the first one helped me a lot today on the back nine.
"I had some feeling of calmness come through. It was very helpful on what has been one of the hardest back nines I've ever played in a tournament.
"It's a dream come true to win two majors in one year. It took me forever just to win one and to have two now is something else.
Schauffele said he had yet to decide what to drink out of the famous trophy, adding: "I'm just curious to see what my dad is going to pick as a first drink to drink out of this.
"He's going to have to figure out what he wants to put in there because he's taking the first gulp out of it."
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