Playing with a support on his right leg following a minor operation less than four weeks ago that cut short his French Open, Djokovic made a solid start and drew first blood in a marathon fourth game.
"I tried to really focus on the game and not think about the knee too much. Everything that I could do, I have done over the last three weeks along with my team to be able to play here for you today," Djokovic said.
"If it was for any other tournament I probably would not have risked it, would not have rushed as much, but I just love Wimbledon, love coming back here.
"I want to thank my surgeon again for doing a great job. Things would be a bit complicated (without successful surgery) to be able to play on the highest level and avoid major injuries has been good.
"I've been fortunate to not be away from the tennis for so long."
The Serb, bidding for a record 25th Grand Slam title to end his trophy drought this year, broke on his sixth attempt and breezed through the opening set under the Centre Court roof before heaping the pressure on Kopriva early in the next.
He let out a big roar having grabbed another break after a 21-shot rally and used it as a platform to double his advantage in the match, as the 123rd-ranked Kopriva struggled to keep pace with last year's runner-up.
The Wimbledon main draw debutant offered resistance early in the third set but was unable to subdue second seed Djokovic, who shifted up another gear to run away with the match.