Serbia’s Djokovic, who lost the Wimbledon final to Alcaraz, won 6-0 6-2 6-3 against France’s Alexandre Muller in Monday’s night session in New York.
Djokovic, 36, was not allowed to play in the United States last year because he was not vaccinated against Covid-19.
He has returned knowing another title will be a record-equalling 24th major.
Matching Australian Margaret Court’s all-time tally is Djokovic’s target and he made a statement start by breezing past 84th-ranked Muller.
“I started tremendously well, we started quite late but nevertheless I was excited to go out on the court – it has been a couple of years,” said Djokovic, who will spend a record-extending 390th week at the top of the ATP rankings.
“In the second and third sets I dropped the level of my serve and I had to work for the points a bit more. Nevertheless I played great and I liked the level.”
Having not started until 23:00 local time, the three-time US Open champion showed he did not want to hang around and only dropped eight points in a 23-minute opening set.
A smiling Muller raised both arms in celebration when he finally got on the scoreboard for 2-1 in the second set but the 26-year-old could not stop Djokovic from moving further ahead.
Muller offered more resistance in the third set before Djokovic won the final four games to wrap up victory in one hour and 34 minutes.
Djokovic, who won the Australian Open and French Open earlier this year, is aiming for a fourth title at Flushing Meadows and will play Spain’s Bernabe Zapata Miralles in the second round. He will return to world number one after the tournament.
Top seed Alcaraz, 20, won his first major at the US Open in Djokovic’s absence last year and starts the defence of his crown against Germany’s Dominik Koepfer on Tuesday.
Alcaraz and Djokovic are the joint favourites for the men’s singles title having developed a fascinating rivalry over the past 12 months.
It was bubbling at the start of the season but without both present at key tournaments there was little chance for the pair to go toe-to-toe on the court.
Now the match-up has ignited over the past few months following three compelling contests in the French Open semi-finals, the Wimbledon showpiece and this month’s Cincinnati final.
Alcaraz and Djokovic cannot meet at the US Open until the final as a result of being the top two seeds.
