The World No.1 took an hour and 14 minutes to end it on Centre Court in a clinical performance, mirroring his opening 6-2, 6-2, win over Bolivian hitter Hugo Dellien.
Despite a decent start from current world number 48 Struff, who served well and stayed with his Serbian opponent early in the first set, Djokovic took care of business quickly and efficiently.
The two matched service game for service game to 4-4 in Set 1 but as soon as the opportunity arose Djokovic pounced.
Leading 5-4 on Struff's serve he turned on the tap to win four straight points and break to love, claiming the first set 6-4.
The break came much earlier in the second set, at 30-15 in game two Djokovic took the point and pumped his fist, letting out a roar with the intensity rising.
There was another roar from the Serb when a lovely cross-court backhand made it three games to one in the second set as Djokovic turned the screw.
Going through his register of brilliant passing shots down the line, carefully crafted drop shots, unreturnable serves and lightning serve-and-volley-attacks, it was all over in an hour and 14 minutes.
The victory made it 6-0 in the head-to-head between these two as the Djokovic juggernaut rolls on.
He will now face Spain's Alejandro Davidovich in the third round.
“It was challenging but I’m pleased to overcome the first hurdle,” said Djokovic.
“I think I was solid on the court. I could always do better but for a first match I’m satisfied.”“It was the hottest day so far. Humidity is brutal. It’s certainly hot but also humid, the hard courts absorb the heat and it stays trapped in there. There was not much wind, not much breeze.”
Djokovic on course for Golden slam
The victory means that the 34-year-old is one step closer to a historic 'Golden Slam' - meaning winning all four major tournaments and an Olympic gold medal in a single year.
No male tennis player has ever managed it, Steffi Graff is the only one to have won all five titles in the same year, in 1988.
Djokovic has already won the Australian and French Open this year as well as the Wimbledon title last month to claim his his 20th career Grand Slam title.
By winning Olympic gold in Tokyo, then the 2021 US Open in August/September, Djokovic would achieve this momentous feat.
"The Olympics and the US Open are obviously my biggest objectives for the remainder of the season, and it’s going to be demanding," Djokovic told Montenegro station MINA.
"But I am full of confidence and motivated to represent Serbia in the best possible way. I am yearning for a medal in Tokyo, hopefully gold, and then I’ll go to New York aiming to complete it all."