NEW YORK—It was easy to see why Novak Djokovic was muttering to himself in between points, staring at his box during changeovers, and smacking his bag with his racquet. Much like Roberto Bautista Agut in the fourth round, Feliciano Lopez, the rare Spaniard who earns his keep with the first shot of each point rather than the sequence that follows it, was giving the heavy favorite all he could handle.

Djokovic had won the opening five games of his late-night quarterfinal inside muggy Arthur Ashe Stadium, but it was still hard for him to feel in control. His opponent’s serve was the most potent, game-breaking stroke between the two, which seems illogical when you consider that Djokovic is the top-ranked player in the world and is generally accepted as the best returner in the game. But Lopez’s smooth, explosive service delivery can obfuscate even a genius ground game—just ask Rafael Nadal, who the soon-to-be 34-year-old beat last month in Cincinnati.

It was a frustrating night for the world No. 1.

“Just frustrating when you drop—you play one sloppy service game in the beginning,” Djokovic said about the second set. “Was 30-Love in that game and I allowed him to break me and the set was gone.”

But it was a victorious night, as well. Djokovic has been beaten by some of the game’s top servers in the past—John Isner has upset him twice, and one of his five losses this year was courtesy of Ivo Karlovic—but he remained patient enough to allow his skill to ultimately dismiss Lopez in four sets, 6-1, 3-6, 6-3, 7-6 (2).

"It's a win in four sets against a player who is in form, playing well in Cincinnati, playing with the confidence, and winning against some top players," says Djokovic, who plays defending champion Marin Cilic next. "All in all, I'm in the semifinals. I have two days off, and hopefully will be able to get ready for the next one."

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Djokovic passes second straight four-set test to reach ninth straight semi

Djokovic passes second straight four-set test to reach ninth straight semi

In watching Djokovic contend with Lopez’s aerial assault, it was hard not to think of Roger Federer, who had a similarly uncomfortable experience the previous evening against Isner. Federer was able to break Isner just once in his straight-sets win, but he tested the big man all night with his block return. It’s a short stab that deflects the server’s pace back; against a player whose mobility is a weakness, it can be very effective.

Djokovic’s return may be superior to Federer’s overall, but perhaps not as much against the tour’s giant servers. There is more nuance in Djokovic’s return; a variety of movements must occur for his strings to collide with the zooming ball at the exact position needed. Both of the top two seeds' returns require impeccable timing, but they are quite different in execution.

In trying to prevent Lopez from serving out the second set, Djokovic reached 0-15. Lopez served a dart. Djokovic tried to hit a bull’s-eye with a risky, uppercut return that looked more like how someone might attempt to impart spin on a forehand. It didn't work. 15-15.

On the next point, Lopez served into Djokovic’s body. The Serb had to both move out of the way and into the return. One of the most underused shots in tennis, the body serve is even more confounding to return when it's hit at Lopez's usual high velocity. Djokovic couldn't get a handle on it. 30-15.

Shortly after, it was game and set to Lopez—and a few whacks at the equipment bag for Djokovic.

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Djokovic passes second straight four-set test to reach ninth straight semi

Djokovic passes second straight four-set test to reach ninth straight semi

This is all to say that Djokovic had difficulty with Lopez’s serve from the moment the No. 18 seed found his rhythm in the second set. Djokovic also fought himself on this evening. He hit just 17 unforced errors, but with so few long rallies, every one seemed costly.

It was a long night for the world No. 1.

“In a match like this against a player who comes in a lot, chips and charges and has a huge first serve, you need to be able to try to reduce your unforced error ratios as much as you can,” said Djokovic.

But it was a successful night, as well. Djokovic fought fire with fire, serving at a good clip of his own. He landed a higher percentage of first serves than Lopez (58 percent to 51 percent) and won considerably more second-serve points (67 percent to 54 percent). He tended to find the clutch shot when absolutely necessary, and he methodically answered Lopez’s holds time and again.

“I started to feel the end of the fourth like my serve, finding the range on my serve, which wasn't working at all in the first part of the match,” said Djokovic.

At 4-2 in the third set, Djokovic trailed 15-40. He saved both break points. At 2-3 in the fourth set, Djokovic stared down another pair of break opportunities. He induced a Lopez error on the first, then snuffed out the second with an ace.

Djokovic broke Lopez just three times on Tuesday night/Wednesday morning, and one of those was due to a double fault on break point. A tiebreaker would determine if this match would become a 2 a.m. marathon, or Djokovic's second straight tough, four-set win. This is when the top seed came up large. He scored two mini-breaks with short backhand returns—much more effective than those described earlier—and he followed each one with a backhand winner. Up 4-1, Djokovic ran out the match with surprising ease considering how close it had been.

"Sport of small margins, especially on the high level," Djokovic said "One or two points can really change the course of the match."