Gauff appeared in big trouble at the outset of the match as the Belgian smartly changed up the pace of her shots to frustrate the teenager, who was broken for a second time when her forehand went long on set point.
Mertens relished her opportunity to play the spoiler in front of a sold-out Arthur Ashe Stadium crowd firmly in Gauff's corner, quieting the increasingly tense fans with a shush finger after smacking winners.
After some exchanges of breaks early in the second set Gauff seized the momentum for good when she broke for a 4-3 lead, pumping her arms and pointing to her ear when her backhand winner levelled the contest at a set apiece.
The third set was all one-way traffic as Gauff's speedy defence, pinpoint serving and terrific play at the net overwhelmed former two-time quarterfinalist Mertens.
Next up for sixth seed Gauff is an enticing first meeting with returning veteran Caroline Wozniacki, who came from behind in similar fashion and by a similar score line earlier in the day to see off American Jennifer Brady 4-6 6-3 6-1.
"It's a matchup I never thought I'd have to play," Gauff said of former world number one Wozniacki, who retired in 2020 to start a family and returned to the game last month.
"When she retired I remember saying that I wish I could have played her. So that wish came true so I'm really excited... She's still fit and going strong. I think it's going to be an exciting match."
On the men's side, Taylor Fritz, Frances Tiafoe, Tommy Paul and Ben Shelton all moved safely through to the last 16, raising hopes of a first homegrown male champion in two decades.
It has been 78 Grand Slams since Andy Roddick won the 2003 US Open and there is growing belief that the talent is there to end the drought of American champions.
Ninth seed Fritz is seen as the main U.S. contender for the title and he blasted his way into the fourth round with a 6-1 6-2 6-0 demolition of 18-year-old Czech qualifier Jakub Mensik.
Tiafoe, who electrified the tournament with his run to the semi-finals last year, is once again exciting the home crowd, advancing with a 4-6 6-2 6-3 7-6(6) victory over crafty French veteran Adrian Mannarino.
Fourteenth seed Paul overcame a third-set hiccup to dispatch Spaniard Alejandro Davidovich Fokina 6-1 6-0 3-6 6-3 and will next face 20-year-old compatriot Shelton, a 6-4 3-6 6-2 6-0 winner over Aslan Karatsev.
"Tremendous," said Tiafoe, summing up the US results so far.
"We're going to continue to do so. This is a group that had a lot of ability. Always had a lot of talent.
"You look at a guy, Tommy Paul, took him a while to get going. He believes more than anybody right now. Taylor obviously has been playing well for a while. Myself. Ben, he's had an up-and-down year, but now he's playing great tennis.
"It's good to see a lot of players playing well. Hopefully we just keep doing it."