Novak Djokovic enjoyed a smooth passage into the US Open quarter-finals as he won in straight sets to end Croatian qualifier Borna Gojo’s remarkable run.

“I did well in the important moments and I’m pleased to get through in three sets,” said three-time winner Djokovic.

The 36-year-old Serb will play ninth seed Taylor Fritz, who is one of three American men in the quarter-finals.

Fritz, 25, won 7-6 (7-2) 6-4 6-4 against Swiss qualifier Dominic Stricker, joining Frances Tiafoe and Ben Shelton in progressing on Sunday.

Tiafoe, 25, beat Australia’s Rinky Hijikata 6-4 6-1 6-4 to set up a last-eight meeting with Shelton, guaranteeing at least one home player in the semi-finals.

Shelton, 20, beat 14th seed Tommy Paul 6-4 6-3 4-6 6-4 as three American men reached the quarter-finals for the first time since 2005.

‘Ready’ Djokovic lies in wait for American trio

Fritz, Tiafoe and Shelton are each bidding to become the first man from the host nation to win the singles title since Andy Roddick in 2003.

In order to for Fritz to emulate Roddick, he will have to find a way past Djokovic first.

Djokovic reached a 57th major quarter-final, leaving him one adrift of Roger Federer’s record in the Open era, with a straight-forward victory over 105th-ranked Gojo.

The manner of the win was a stark contrast to the fightback from two sets down which he had to perform against fellow Serb Laslo Djere in the previous round.

Djokovic did not concede a break point to US Open debutant Gojo in the opening set, but lost his serve for 2-0 in the second set by planting a volley into the net.

However, 25-year-old Gojo was unable to consolidate. The big-serving Croat hit five double faults as he handed over the game without making Djokovic apply too much pressure.

Djokovic continued to nullify Gojo and smartly took care of his own service games, breaking three more times as Gojo became increasingly weary and took a third match point with an ace out wide.

“I knew Borna has a big game and is a big-shot player. One of the keys to the match was reduce his serve and stop the aces,” said Djokovic.

“I tried to manage my energy and focus on accuracy with my serve.

“The matches are obviously going to get tougher but I’m ready.”

Smiling Shelton wants to inspire young fans

Shelton hopes he can inspire young people to “develop a passion for tennis” after an impressive win over Paul which featured two 149mph serves.

The pair of aces were just short of the tournament-record 152mph thunderbolt which Roddick hit on his way to the title 20 years ago.

“I’m not just a tennis player. I don’t just put on a show on the court or win a lot of matches,” Shelton said.

“I treat people the right way and make an impact on a lot of young kids.

“I hope there’s a lot of young people in the crowd that develop a passion for tennis when they watch me play.”

On the 149mph serves, he added: “That’s cool, but I’m also not out there to chase the miles per hour. I’m trying to effectively hold serve.

“It hurt me a little bit today hitting 149, 141 and then 149 again. I got broken my next two games. Sometimes when I’m chasing a number or I try to hit harder than is within myself, it messes up my rhythm.”

Shelton’s style seems made to inspire and, after overcoming a nervy start that saw him quickly go 3-0 down in the first set, his power and relentless desire to take the aggressive option quickly got the New York crowd on side.

“You can’t deny that presence. It rubs off on anyone,” said tennis correspondent Russell Fuller on BBC Radio 5 Sports Extra.

“You’d have to be a cynical old hack if you weren’t moved by the way Ben Shelton plays tennis. He plays with such a smile on his face.”