But he had to recover from early breaks in both of the first two sets against a player who beat him at Indian Wells this year, as well as a nasty fall on the Centre Court grass.
Japan's Naomi Osaka is the only player to have triumphed twice since the start of 2017, although the US Open and Australian Open champion struggled to cope under the spotlight of being the top seed at the French Open, saying she suffered headaches from the "stress" before going out in the third round.
"I called Goran and asked him whether he's available to come to Wimbledon and sort of give it a try, and have a little bit of a trial type of tournament where we get to know each other and see how it works", said Djokovic.
His 18th career major also meant he moved within two Slams of Federer's all-time mark for the first time.
The champion made an inauspicious start, double-faulting his first serve en route to being broken, but quickly found his feet to reel off the next four games and win the first set 6-3.
The 34-year-old needs a Wimbledon title to complete his career Grand Slam and while, for whatever reason, he has never thrived on the All England Club lawns, he looked razor sharp as he began his 15th successive appearance.
At 4-4 the German saved three break points - the last courtesy of a successful challenge - only to drop his next service game as Djokovic served out for 7-5 and a two-set lead.
Goalie Keith Kinkaid signs with Montreal Canadiens, excited to back up Price
Waddell, meeting with the media at 3 p.m., said the team received word of the offer sheet just 20 minutes earlier. An offer sheet worth more than $10,568,589 per season would return compensation of four first-round draft picks.
He said: "It felt great to be back".
He wound up running his Grand Slam winning streak to 26 matches before losing a five-set tussle against Dominic Thiem at the French Open in early June. First opening rounds are obviously tricky if you get a quality opponent like Kohlschreiber, who has got a lot of experience.
Three-time grand-slam victor Stan Wawrinka made short work of Belgian Ruben Bemelmans, the Swiss roaring to a 6-3 6-2 6-2 victory in less than an hour and a half to book a second-round match with American Reilly Opelka.
But Federer is quick to praise the influence of Djokovic and Nadal - between them, the trio have won 53 of the last 64 Slams.
Kevin Anderson and Stan Wawrinka have also progressed to the second round.
Roger Federer faces Lloyd Harris.
The straight-sets win came as a huge relief to fourth seed Anderson considering Herbert appeared to be in fine form on grass having reached his first tour level semi-final on the surface at the Halle warm-up tournament. The South African will face Serbian Janko Tipsarevic next.