Djokovic, prevented from playing in last year's US Open due to being unvaccinated against COVID-19, began his latest campaign to match Margaret Court's all-time record haul of 24 Grand Slams with a 6-0 6-2 6-3 win over Alexandre Muller.
Arriving in New York on the back of an absorbing win over young rival Carlos Alcaraz in the Cincinnati final, an in-form Djokovic showed the 84th-ranked Frenchman no mercy in his US Open main draw debut.
"This court has seen so much history and so many battles," Djokovic told the New York crowd.
"Everyone knows in tennis that night sessions at Arthur Ashe definitely are the most exciting, fun, loud, energetic sessions you can have out there in the tennis world."
While the US Open has just got underway, Djokovic's win guarantees he will nudge Alcaraz out of top spot in the rankings when they are updated on September 11.
Djokovic had not been seen on the Flushing Meadows hard courts since his loss to Daniil Medvedev in the 2021 final and fans let the Serb know they had missed him, showering him with applause as he emerged from the tunnel.
And it was clear that the three-time champion had missed them too as he embraced the cheers of a record crowd of over 30,000 that included former US President Barack Obama and his wife Michelle.
The US Open also welcomed back fan favourite and twice finalist Wozniacki, who retired in 2020 to raise a family and marked her return to Grand Slam tennis with a tidy 6-3 6-2 win over Russian qualifier Tatiana Prozorova.
It has been 78 Grand Slams since Andy Roddick won the 2003 US Open and hopes that an American man can snap that title drought have fallen largely on the shoulders of Fritz and Tiafoe.
The top-ranked American men were hardly tested on Monday, with ninth seed Fritz crushing compatriot Steve Johnson 6-2 6-1 6-2 and Tiafoe, the 10th seed, beating another American, Learner Tien, 6-2 7-5 6-1.
Christopher Eubanks, who grabbed the limelight with an unexpected run to the Wimbledon quarter-finals, was also a popular winner with the home crowd after he beat South Korea's Kwon Soon-woo 6-3 6-4 0-6 6-4.
Sixth seed Gauff, winner in her final US Open tune-up in Cincinnati, got off to a nervy start and had to fight back against feisty German Laura Siegemund before advancing 3-6 6-2 6-4.
In contrast to Gauff's laboured win, Danielle Collins, the 2022 Australian Open finalist, turned on the jets to dispose of Czech Linda Fruhvirtova 6-2 6-0 in a lightning-quick 52 minutes.
