The world number one, who is chasing a sixth title in New York, was never really troubled during a 6-3 6-2 6-4 victory over America's Donald Young.
Federer has been in great form this summer, winning his seventh Wimbledon title and reaching the final of the Olympics, while he defeated Djokovic to win the Masters Series tournament in Cincinnati last weekend.
But the 30-year-old feels the Serb's status as the defending champion and his back-to-back wins over him in semi-finals at Flushing Meadows give the second seed the edge.
Federer said: "Novak to me goes in as the favourite still because he's the defending champion. He's probably won the most titles on hard courts the last couple of years. It's where he felt most comfortable.
"He's beaten me the last couple of years as well. Then again, I've had a great summer. So has (Andy) Murray. It's going to be an interesting US Open. I'm happy I'm through the first round."
In contrast to the form of his opponent, 23-year-old Young last week ended a run of 17 straight defeats stretching back to February, the third longest in the Open era.
Young reached the fourth round here last year, eventually losing to Murray, and gave a decent account of himself on Arthur Ashe Stadium without ever really threatening an upset.
Federer made his move in the eighth game of the first set, breaking to love and then serving out the set, and he was soon a break up in the second set.
Young earned a huge cheer from the crowd when he levelled at 2-2 but parity was brief before the top seed streaked away again and he completed victory in an hour and 34 minutes.
Olympic champion Murray earlier overcame some poor serving and a touch of cramp to book his place in the second round.
In the end the third seed was a comfortable 6-2 6-4 6-1 winner over Russia's Alex Bogomolov, but not before he had lost his opening two service games and fought back from a break down in the second set.
It took two hours and 15 minutes for Murray to wrap up victory on a hot and humid day on Arthur Ashe, and he struggled a little with cramp in the final stages.
Murray said: "I won in three sets. I didn't serve very well. I only lost seven games in three sets, so I must have done something well.
"I think Bogomolov was seeded here last year. He made the third round. He plays his best tennis on the hard courts. He's a tough player.
"I played fairly well from the back of the court. I just would have liked to have served a bit better because I wasn't getting many free points on my serve. Because of that, there were a lot more rallies. When he's in a rhythm, he's tough to break down.
"It was very, very hot and tough conditions. You want to try to win the matches as quickly as possible."
A heavy thunderstorm earlier in the day had put the matches behind schedule but there was plenty of home success for the fans to cheer, with Mardy Fish, James Blake and Jack Sock all reaching the second round.
Fish, the 23rd seed, had to scrap for a straight-sets win over Japan's Go Soeda, taking more than two and a half hours to come through 7-6 (7/3) 7-6 (7/2) 6-3.
Blake and Sock are at opposite ends of their careers, with Blake one of the veterans of the ATP Tour at 32 while Sock is still a teenager.
The 19-year-old benefited from the retirement of 22nd seed Florian Mayer, who called it a day with the American leading 6-3 6-2 3-2, while Blake defeated Slovakia's Lukas Lacko 7-5 6-2 3-6 6-3.
It was generally a good day for the seeds, with Fernando Verdasco, Kei Nishikori, Jeremy Chardy, Feliciano Lopez and Marcel Granollers all winning.