Executing a game plan of controlled aggression, the Spaniard defeated Safiullin, 6-4, 6-4, 6-4. Alcaraz revealed no lingering effects from a wrist injury that kept him out of the last two Grand Slams.
Alcaraz acknowledged feeling "some doubts" heading in, but told a courtside interviewer he was thrilled to be back in New York, where he won his first of seven Grand Slams.
"I missed the crowd, I missed the energy, I missed competition, I missed everything," he said. "I'm really happy to compete again."
A powerful baseliner with a prior win over Alcaraz, Safiullin kept close in all three sets, but never looked likely to threaten the Spaniard.
The match was even at 3-3 when Alcaraz snagged a break with a big forehand, the signature weapon he used to take control of many of the longer rallies.
Safiullin broke early in the second set, but Alcaraz, moving well and breaking up rallies with surprise drop shots and occasional serve and volley plays, quickly broke back and broke again.
He broke early in the third set and never looked back.
A two-time winner in New York, Alcaraz is normally at the top of the list of favorites in the game's biggest events.
But the Spaniard's form looked uncertain when he pulled out of the Cincinnati warmup event, opting to make his return to play at a Grand Slam with best of five set matches.
"I'm pretty sure I'm going to get better and better every day," Alcaraz said after the match.
"The most important thing I'm proud of was mentally I was able to deal with the doubts."
