Five-times champion Federer ran through his full array of shot-making as he dismissed American Donald Young 6-3 6-2 6-4 to reach the second round.
Having won his 17th Grand Slam title with his victory at Wimbledon last month, Federer is many people's pick to add a sixth US Open crown to his ever-growing resume.
But the Swiss said the efforts of Serbia's Djokovic in recent times gave him the edge.
"I still think Novak is the favourite for the title coming in here," Federer said after his one hour, 34-minute victory under the lights.
"He's the defending champion, he's probably won more hard court titles than anyone in the last few years and he also beat me here in the last two years."
Federer was untroubled by windy and humid conditions at Flushing Meadows as he made world number 81 Young look distinctly second-rate.
The American was once tipped for greatness as a teenager but his win in the first round in Winston-Salem last week snapped a 16-match losing streak that saw him plummet down the rankings.
The left-hander has plenty of talent but Federer just absorbed everything he could throw at him and gave it all back, and more.
The Swiss looked in a hurry to get off the court and reeled off his full array of strokes to set up a second-round encounter with Bjorn Phau of Germany.
"I think it was a good start in difficult conditions," Federer said.
"He was a talented opponent and I'd never played him before but it was good."
In other action, 17th seed Kei Nishikori encountered few problems on his way to a 6-1 6-2 6-4 win over Argentina's Guido Andreozzi.
Nishikori's Japanese compatriot Go Soeda was not as impressive, going down 7-6(3) 7-6(2) 6-3 to American 23rd seed Mardy Fish.
Another American, Jack Sock, managed to progress after his opponent, the 22nd seeded Florian Mayer of Germany, retired hurt when 6-3 6-2 3-2 down.
Spanish trio Fernando Verdasco, Marcel Granollers and Feliciano Lopez all won through to the second round.
Verdasco, the 25th seed, beat Portugal's Rui Machado 6-1 6-2 6-4, 24th seed Granollers downed Denis Kudla of the US 6-3 4-6 6-3 7-6(2) and Lopez saw off Dutchman Robin Haase 6-3 7-5 6-2.
In late-finishing matches, 16th seed Gilles Simon recovered from two sets down to beat Michael Russell of the US 7-6(4) 3-6 5-7 6-4 6-1 while12th seed Marin Cilic also battled back from a two-set deficit to see off Australian Marinko Matosevic 5-7 2-6 6-4 6-2 6-4.
Completing the seeds in action on the opening day was Jeremy Chardy, the 32nd seed from France, who beat Italian Filippo Volandri in straight sets 6-3 6-4 6-3.