Top seed Federer, playing in his 52nd consecutive Grand Slam tournament, brushed aside 81st-ranked Young, who only last week stopped a run of 17 defeats in a row but who now stands at three wins and 22 losses in 2012.
Federer, who won his 17th Grand Slam trophy courtesy of his seventh Wimbledon title in July, goes on to face German veteran Bjorn Phau for a place in the last 32.
The Swiss star's win was also the first step on his way to erasing the disappointment of 2011, when he squandered a two-sets-to-love lead and match points to lose to eventual champion Djokovic in the semi-finals.
And he remains wary of the danger posed by his great Serb rival.
"For me, Novak goes in as the favourite because he's the defending champion. He's probably won most titles on hard courts in the last couple of years. It's where he feels most comfortable," said the world number one.
"He's beaten me the last couple of years here as well. It's strange for me to be the favourite just after beating him a couple of times."
Djokovic stands to win the biggest pay day in the history of tennis of $2.9 million if he wins the New York title, his prize money bolstered by a $1 million bonus for his overall success in the US Open build-up events.
Although he trails Federer 16-12 in their head-to-head meetings, and lost at Wimbledon as well as the final in Cincinnati last week, Djokovic beat Federer in the semi-finals of the US Open in 2010 and 2011.
Federer, who reclaimed the world number one ranking after an absence of two years following his win at Wimbledon, is adamant that staying at the top is not his priority.
"I am happy to be world number one, but it's not what drives me during this year's US Open," he said.
"It's actually trying to get the title or get closer to that title because first the focus is completely elsewhere."
Federer won five titles in succession in New York from 2004 to 2008, but was runner-up to Juan Martin del Potro in 2009 before Rafael Nadal and Djokovic claimed the two most recent editions.
Young, meanwhile, will see his world ranking slump to around 120 next week as a consequence of his failure to match his best performance at a major, a run to the last 16 at the US Open in 2011.
But Federer had words of encouragement for the defeated American.
"He's a great player, but maybe he needs to understand the tour more, about the grind of the outside courts," said the world number one.
"But there's no way past the hard work, day in, day out."