The 57th-ranked American defeated a top five player for the first time in his career, saving all six break points he faced while firing seven aces against the Greek.
American delivers stunning performance in career-best win
Tiafoe earned two break points in the opening game of the match, but only needed one when Tsitsipas flew a backhand long to hand the American the early lead.
The Greek, finalist at Roland Garros, earned a break point of his own, but a big serve and forehand got Tiafoe out of trouble and he held for a 3-1 advantage.
A sensational forehand over his shoulder highlighted the eighth game to give the world number 57 a 5-3 edge and he would close out the set two games later.
The second set was going along on serve, Tiafoe with a nice approach and backhand volley gave him a hold that brought the score to 2-2. Both men were serving well until the ninth game.
There, Tsitsipas saved two break points, but a ripping forehand gave Tiafoe a third opportunity and he extracted a backhand error from the Greek to take the lead and another miss on the backhand gives Tiafoe a two-set lead.
The world number 57 broke to open up the third set when Tsitsipas smashed a volley into the net. Brought to deuce several times in the fourth game, Tiafoe held to stay in front 3-1.
Big serving again got the American through another game, this time to give him a 4-2 lead. Saving two break points, Tiafoe was a game away holding a 5-3 advantage.
Serving to stay in the match, Tsitsipas fell behind 0-40 and although he saved the first two match points, a final netted backhand ended the match, giving Tiafoe a superb victory.