Australian Open champion Sinner kicked off his campaign at the year's final major with a 2-6 6-2 6-1 6-2 victory over American Mackenzie McDonald in New York on Tuesday (Wednesday AEST).
Sinner became embroiled in controversy in the week before the Open started after the International Tennis Integrity Agency said that he tested positive twice for an anabolic agent in March.
The Italian, who has denied wrongdoing, has been under intense scrutiny in New York and was slow out of the starting blocks.
He committed several unforced errors in the opening set, which McDonald took full advantage of to claim an early lead.
The American broke early in the second set to take a 1-0 lead, but after spurning three break points in a lengthy game, Sinner levelled at 1-1.
The hard-fought break appeared to fill the world No.1 with confidence and the tide of the contest turned as he raced to a 4-1 advantage, before holding serve and breaking once again to square the match at a set apiece.
Sinner never looked back from there and won five games in a row to take the third before winning the first three games of the fourth set without dropping a point.
McDonald won a couple of games late in the match to delay the inevitable, but Sinner made his advantage count and served out the set to claim an emphatic victory.
"It started not in the best way, but you know, the first matches in every tournament are not easy, you have to accept it," Sinner said in his on-court interview.
"He played really, really well in the beginning and I tried to stay there mentally and tried to get into rhythm, which I've done at some point in the second set and then just tried to keep going. I'm very happy to be in the next round.
"We go day by day. Tomorrow I have one day off where we will try to get a little bit more rhythm and improve for the next match."
Sinner's win was his first on Arthur Ashe after a few disappointing defeats, including his five-set loss to Alexander Zverev in the fourth round last year.
The 23-year-old faces another American, Alex Michelsen, in the second round.
In other first-round action, Britain's Dan Evans came through a marathon contest lasting five hours and 35 minutes, the longest ever match of the tournament in the professional era, to beat 23rd seed Karen Khachanov 6-7 (6-8) 7-6 (7-2) 7-6 (4-7) 4-6 6-4.
Russian fifth seed and former champion Daniil Medvedev overcame a second-set wobble to beat unseeded Serbian Dusan Lajovic 6-3 3-6 6-3 6-1.
Czech 18-year-old Jakub Mensik knocked out Felix Auger Aliassime, beating the Canadian 19th seed 6-2 6-4 6-2 to advance to the second round.
Jack Draper reached the second round after his Chinese opponent Zhang Zhizhen retired with a left leg injury in the third set with the Briton leading 6-3 6-0 4-0.
Frenchman Arthur Fils beat American Learner Tien in four sets, 6-4 3-6 6-1 6-2, and 16th-seeded American Sebastian Korda scored a crushing 7-6 (7-3) 6-1 6-0 victory over Corentin Moutet, of France.
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