After five-set battles in his opening two matches, Federer only needed an hour and 46 minutes to dismiss Feliciano Lopez 6-3 6-3 7-5.
The third seed’s movement was much improved and he made far fewer unforced errors as he set up a last-16 clash with German Philipp Kohlschreiber.
Federer had perhaps simply had enough of waiting, with three long day session matches – the last of them another battle for Rafael Nadal – meaning the night session started two and a half hours late.
More than 20,000 ticket-holders had been left outside in the rain while Nadal finished off his four-set win over Leonardo Mayer.
It was a full house and a lively atmosphere, and the fans were more than happy with a paucity of drama if it meant seeing Federer back to free-flowing normality.
His protestations that his suspect back was feeling just fine after battles against Frances Tiafoe and Mikhail Youzhny rang a little hollow but there was certainly much more of the player who did not drop a set at Wimbledon in this performance.
After extending his winning record to 17-0 against Youzhny, Federer met another old sparring partner in 35-year-old Lopez, who he had beaten 12 times in a row.
The pair combined to make this the oldest US Open clash since Jimmy Connors faced Ivan Lendl 25 years ago.
On that occasion, 32-year-old Lendl beat 39-year-old Connors, but here the older man was on top from the start, needing just 25 minutes to win the opening set.
Lopez had several chances in the second but could not take them, and he looked doomed when Federer broke early in the third.
The 36-year-old Swiss played his one really loose game of the night to drop serve immediately but seized his chance when it came in the 12th game, clenching his fist in delight.