Djokovic had endured a far more testing match on Friday, having to come back from two-sets down against Laslo Djere to keep alive his bid for a fourth US Open title that would see him match Margaret Court's record haul of 24 Grand Slams.
On Sunday, the Serb broke to open the contest and was never threatened as Gojo managed only a single break chance in the entire match.
Djokovic committed just 12 unforced errors compared to 40 by the 105th-ranked Croat, who was under constant pressure and had his serve broken five times before the second seed closed out the contest with his 12th ace.
"I was watching him play qualifications, last couple of rounds of the main draw, and saw that he's a big shot player," said Djokovic after his 98th career match at Flushing Meadows, where he trails only Jimmy Connors (115) and Roger Federer (103).
"Obviously serve and forehand big weapons. He moves pretty well for a big guy.
"In a best-of-five sets I try to manage my energy and focus on accuracy with my serve.
"I think I've done well in important moments and just glad to get through in straight sets."
Next up for Djokovic is top-ranked American and ninth seed Taylor Fritz, who advanced with a tidy 7-6(2), 6-4, 6-4, win over Swiss qualifier Dominic Stricker.
Fritz will head into the showdown as the only player yet to drop a set but still stinging from the 6-0, 6-4 beating Djokovic laid on him in the quarter-finals of the Cincinnati Open.
"Obviously Taylor has been now an established top-10 player for the last couple of years," said Djokovic, who has won all seven career meetings with Fritz. "He has been playing some terrific tennis, particularly on home soil on hardcourt tournaments.
"He has improved so much over the years so, obviously the matches are only going to get tougher from now onwards and I'm ready for the challenge.
"It's going to be great."
