Djokovic, seeking to equal Roger Federer’s men’s record of eight singles titles at SW19, beat Vit Kopriva 6-1 6-2 6-2 under the roof on Centre Court.
The Serb, 37, had an operation on a torn medial meniscus on 5 June, having aggravated the problem during the French Open.
He will next play British wildcard Jacob Fearnley.
Wearing a knee support on his right leg, Djokovic showed no signs of discomfort against the 27-year-old Czech qualifier, converting his sixth break point in a lengthy fourth game before racing through the rest of the first set.
He broke again early in the second set, stretching his right leg out to stay in a rally and then, in trademark style, converting defence into attack and forcing Kopriva into going long.
Three further breaks of serve hurried him to victory, Djokovic finishing the match with three consecutive aces as he moved to the next round in style.
“I tried to really focus on the game and not think about the knee too much,” the 24-time Grand Slam champion added in his on-court interview.
“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. I think 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.”
