The victory also moves Djokovic into his 64th grand slam quarter-final, extending his all-time record, and keeps alive his pursuit of a record 25th major title.
Four-times US Open champion Djokovic dominated from the opening game, breaking the 35-year-old German's serve six times during the 109-minute fourth-round match on Sunday night.
"I don't know how many more I'm going to have, so obviously each one is very special and I want to thank all you guys for being present here tonight," Djokovic said
Qualifier Struff, ranked No.144, had defeated two seeded players to reach his first US Open fourth round but was unable to put any serious pressure on the Serb.
Djokovic required treatment from the physio on his right shoulder and forearm during changeovers but did not appear overly troubled by the issues and won 79 per cent of his first-serve points.
He will now face last year's runner-up Taylor Fritz, the lone American left in the men's draw, who swatted aside Czech Republic's 21st seed Tomas Machac 6-4 6-3 6-3.
Djokovic has a 10-0 head-to-head record against Fritz, who is trying to his country's 22-year wait since Andy Roddick lifted the trophy in 2003.
Earlier, second seed Carlos Alcaraz put on a show in a convincing 7-6(3) 6-3 6-4 win over France's Arthur Rinderknech in his latest demolition job on Arthur Ashe Stadium.
The 22-year-old Spaniard belted 36 winners and had just 11 unforced errors as he reached his fourth grand slam quarter-final of the year, setting up a clash with Czech 20th seed Jiri Lehecka.
The 2022 champion got the crowd on his side with a behind-the-back shot in the fourth game and put his foot on the gas to pull away in the tiebreak with a pair of exquisite forehand winners and an unreturnable serve.
"Sometimes, I practice it. I'm not going to lie," said Alcaraz of the behind-the-back effort.
Just in practice, if the opportunity is there, I will try. In the match, it's kind of the same. If I have the opportunity, why not?"
Lehecka advanced to his second slam quarter-final with a 7-6 (7-4) 6-4 2-6 6-2 win over Adrian Mannarino.
But Alcaraz will take a lot of stopping.
"My style of tennis suits pretty well to the energy here in New York," said Alcaraz, the winner of five grand slam titles.
"The energy is special playing the day session, playing the night session, it doesn't matter."
