"Looking ahead, it definitely looked like a very tough draw in the first round," Federer said about the prospects of facing the 34th-ranked Argentine, who had five match points against him last year in Shanghai before falling.
Seventy-seven minutes after the opening serve at Arthur Ashe Stadium, the 34-year-old Federer walked away from the Flushing Meadows heat with a glow from his 6-1 6-2 6-2 victory.
"I feel good now," said Federer, who is seeking a sixth U.S. Open triumph to add to his record 17 grand slam singles titles.
"I actually wasn't so confident yesterday and today. I just felt like maybe could be one of those matches I just couldn't see coming."
Federer, whose fluid grace and inventiveness on the court make his game seem so natural, revealed some of the calculations he does in preparing for an opponent.
"Thankfully I took this match extremely serious. I thought at times almost I was taking it a bit too serious. I got lucky in Shanghai, so that's why ... it was just creeping around in my mind that maybe today was going to be a bad day.
"Plus I had practiced with him here ... the day of the draw, and he was playing very well in practise, too."
Federer decided Mayer could be dangerous when given time to set up his shot, so he decided to rush him into mistakes.
"Today was much faster than Shanghai. It's a different place and different conditions. It allowed me to play fast-court tennis against him, which wasn't really the case in Shanghai."
Federer has of late been selectively taking advantage of second serves to charge in with a half-volley to apply surprise pressure. He used it to advantage again on Tuesday.
"The good thing is when you do it, you have to play committed. There's no way around it. So when you do it, you're fully committed ... I kind of really like it, because whatever is committed in tennis is a good thing," said Federer.
Playing aggressively, Federer has reached the finals of his last three events, including Wimbledon, where he lost to world number one Novak Djokovic, and a U.S. Open tune-up in Cincinnati where he beat Djokovic for the title.
Asked if he may be playing his best tennis, Federer said: "If I win the tournament here yes, maybe."
(Editing by Frank Pingue)
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