The win was the 18-year-old American's seventh in a row to start the season following her dominant title run in Auckland last week where she lost just 22 games in five matches.
Gauff saved six of seven break points in an opening set that lasted 43 minutes and took a 4-2 lead in the second only to watch as the Brit rallied to force a tiebreaker that the American won.
Neither player was particularly sharp as Raducanu hit 17 winners to Gauff's 13, but also finished with 42 errors to her rival's 41 in the one-hour, 42-minute contest.
Gauff wins battle of teenage sensations
Raducanu was the first to feel pressure, falling behind 0-30 in her opening service game before winning four straight points with some heavy shots to even the set at 1-1.
After saving two break points on her serve, Gauff used her backhand to race out to a 0-40 advantage with the Brit serving. After saving one break point, Raducanu rushed a backhand and was broken.
A break back from Raducanu was followed by another break from the American as the 2021 US Open was wild with a forehand to give Gauff a 4-2 lead.
Serving for the set at 5-3, the seventh seed had to fend off three break points using her heavy serve, a shot that has greatly improved since last year, to close out the opening set.
While both players improved their level of play, it was Gauff that struck first in the second set as and a second double fault in the game gives the American a 2-1 advantage and a commanding position in the match.
It looked to be a routine victory until a forehand into the net by Gauff on break point got Raducanu back on serve at 4-4. Both players would hold out, although the Brit held a set point at 5-4, sending the set to a tiebreaker.
After losing the opening point of the breaker, the American won a 17-shot rally that started a run of four straight points that put her in front 4-1.
In front 6-2, Gauff held four match points and after wasting the first two, she converted on her third with a fabulous lob that Raducanu could only dump into the net.