The third-seeded Djokovic routed No. 19-seeded American Mardy Fish, 6-3, 6-4, 6-1, yesterday, sapping the energy from both his opponent and the nearly packed Arthur Ashe Stadium and leaving only one American man in the draw at the US Open.

Djokovic, eyeing his third straight US Open semifinal, will play No. 17 Gael Monfils in the quarters. Earlier, Monfils beat fellow Frenchman Richard Gasquet, 6-4, 7-5, 7-5.

Since a five-set scare in the first round, Djokovic hasn’t dropped a set. Against Fish, who has played two five-setters in addition to doubles over the first week, the Serb was the better, fresher player.

“I’m playing with a lot of confidence,’’ Djokovic said. “It’s definitely great to raise the level of performance toward the end of the tournament. It’s been a great couple years for me in New York. Hopefully, I can go on.’’

With Fish’s exit, No. 20 Sam Querrey is the only American left in the men’s draw. Querrey faces No. 25 Stanislas Wawrinka today in the fourth round and is the last hope for the United States to break a seven-year drought without a champion at the US Open.

With countrymen Andy Roddick (the last American man to win the title) and John Isner already gone, Fish was hoping to make Labor Day something memorable for his country — an underdog trying to get some momentum, and the crowd, on his side early, maybe channel his inner Jimmy Connors and turn the stadium into his personal cheering section.

That never came close to happening against Djokovic, who dictated most points from the baseline and wound up with 30 winners to 13 for Fish. The occasional shout of “Don’t give up, Mardy’’ echoed from the stands, but mostly, this was a flat afternoon and Fish couldn’t do much to perk things up.

Djokovic’s next opponent is Monfils, who brings his own special flair — and his dreadlocks — to the court.

The Frenchman, who has long professed his love for New York, got the crowd in Armstrong Stadium behind him, then overcame a break in the third set to close out his win over Gasquet in straight sets.

“He [doesn’t] like to see the opponent show emotions,’’ Monfils said. “Just play with that, play a bit with his mind, and that was it.’’

In a night match, five-time champion Roger Federer beat 13th-seeded Jurgen Melzer of Austria, 6-3, 7-6 (7-4), 6-3, to reach the quarterfinals at a 26th Grand Slam tournament in a row.

Before the Fish match, Dominika Cibulkova upset No. 11 Svetlana Kuznetsova, 7-5, 7-6 (7-4), to make the quarterfinals. Ranked 45th, the Slovakian is the lowest-ranked player left in the woman’s draw.

Kuznetsova was the two-time Grand Slam champion in yesterday’s match but didn’t look it. The Russian had 10 double-faults and 42 unforced errors. Kuznetsova reached a second US Open final in 2007 but hasn’t made it beyond the fourth round since.

“I think she plays good, but my level is higher, and I have to win these matches,’’ Kuznetsova said.