The world number one, widely expected to enjoy another trouble-free run to this year's final, was given a stern examination by 35-year-old German Kohlschreiber.
But Djokovic, opening proceedings on Centre Court, recovered from the early blip to run out a 6-3 7-5 6-3 winner.
After blotting his copy book in game one, order was restored as Djokovic broke straight back, and he repeated the trick on his way to taking the first set in 38 minutes.
The second set began in identical fashion, Kohlschreiber breaking the Djokovic serve only to immediately drop his own.
Kohlschreiber, who beat Djokovic earlier this year in Indian Wells, fended off three break points to hold for 4-4, but the 15-time grand-slam winner stepped up a notch and found a way through at the end of the set.
It was a valiant effort from Kohlschreiber, but as Djokovic settled into the match suddenly points against his serve were becoming increasingly scarce.
The 32-year-old cranked up the pressure and two breaks from 3-3 in the third ensured he prevailed in just over two hours to set up a meeting with American world number 111 Denis Kudla in round two.
Men's Wimbledon round-up
Sixth seed Alexander Zverev was a shock opening-day casualty, going down in four sets to qualifier Jiri Vesely.
German Zverev, seen as a potential future grand slam champion, slumped 4-6 6-3 6-2 7-5 on Court One.
The 22-year-old slipped at a crucial moment to give away two match points, and then netted the first as Czech Vesely, ranked 124 in the world, celebrated a memorable win.
Another of the so-called 'next generation', seventh seed Stefanos Tsitsipas, quickly followed Zverev out of the tournament.
The 20-year-old from Greece saved two match points in the fourth set against Thomas Fabbiano of Italy, but was eventually beaten in five 6-4 3-6 6-4 6-7 (8) 6-3 .
Last year's runner-up Kevin Anderson eased into round two after a straight-sets win over Pierre-Hugues Herbert.
The big-serving South African, who 12 months ago shocked Roger Federer in the quarter-finals and then came through a marathon five-setter against John Isner, won 6-3 6-4 6-2.
Frenchman Herbert can now at least turn his full attention to the doubles, where he has linked up with Andy Murray.
Three-time grand slam winner 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.
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