Djokovic and Gauff headlined the action on Arthur Ashe Stadium, where American Ben Shelton got the ball rolling with a 6-4, 6-2, 6-2 victory over 2020 champion Dominic Thiem.
Shelton's triumph marked an end to Thiem's Grand Slam career, the Austrian having announced he would retire at the end of 2024 after several injury-plagued seasons.
"I just want to say thanks for all the support," Thiem told fans. "It's been 10 years since I first played here, I had my greatest success on this court."
In other early action, Olympic women's singles gold medallist Zheng Qinwen of China rallied from a set down to beat Amanda Anisimova 4-6, 6-4, 6-2.
Zheng, seeded seventh, next faces Erika Andreeva of Russia, who beat China's Yuan Yue 6-3, 7-6 (9/7).
"Every ball (from Anisimova) went inside in the beginning and I couldn't do anything," said Zheng, the seventh seed who will next face Russian Erika Andreeva, a 6-3, 7-6 (9/7) winner over China's Yuan Yue.
"Little by little I started to get into the rhythm," added Zheng, who finished runner-up to Aryna Sabalenka at the Australian Open, and could face the second seed from Belarus in the quarter-finals in New York.
Men's fourth seed Alexander Zverev of Germany needed four sets to get past lucky loser Maximilian Marterer 6-2, 6-7 (5/7), 6-3, 6-2.
Olympic silver medallist Donna Vekic of Croatia moved smoothly into the second round with a 6-4, 6-4 victory over Australian qualifier Kimberly Birrell.
But the opening day spotlight was on Djokovic and Gauff.
Djokovic, seeded second behind world number one Jannik Sinner, is vying to become the first man to repeat in New York since Roger Federer won five straight US Opens from 2004-2008.
"Hopefully that changes this year," Djokovic said.
It's been an erratic year for Djokovic, who was hindered by a knee injury and is looking at the prospect of a year without a Grand Slam title for the first time since 2017.
The 37-year-old, whose 24 Grand Slam titles are tied with Aussie legend Margaret Court for most all-time, says he still gets pumped up for the "pillars of our sport."
Under the lights
And that's especially true of the US Open, where he'll anchor the night session taking on Moldovan qualifier Radu Albot.
"I can't wait to be under the lights," Djokovic said. "The noise, the energy of the stadium is just different from anything else."
Gauff, who has endured a dip in form since winning her maiden major last year, closes the afternoon session on Ashe taking on 66th-ranked Varvara Gracheva of France.
Other notable matches on Monday saw second-seeded Sabalenka taking on Australian qualifier Priscilla Hon and Wimbledon champion Barbora Krejcikova of Czech Republic facing Spain's Marina Bassols Ribera.
With US men out to end a US Open title drought that stretches back to Andy Roddick's 2003 victory, Shelton was followed on court by compatriots Taylor Fritz and Frances Tiafoe.
Fritz, the 12th seed, taking on Camilo Ugo Carabelli and 20th seed Tiafoe -- coming off a runner-up finish to Sinner at the Cincinnati Masters -- facing Aleksandar Kovacevic.
