Defending champion Djokovic won 6-0 6-3 6-4 in one hour and 53 minutes to book a last-16 clash with Dutch wild card Tim van Rijthoven.
The 20-time grand slam winner will carry out due diligence on Wimbledon rookie Van Rijthoven, who is through to the fourth round on his debut and has reeled off eight successive wins.
Van Rijthoven won the Rosmalen Grass Court Championships in the lead-up to this fortnight, stunning world number one Daniil Medvedev in the final.
Yet on the form that saw Djokovic crush Kecmanovic's hopes, Van Rijthoven will surely stand little hope of going any deeper into the tournament.
Djokovic won 88 per cent of points when landing his first serve in court, and he has now reached the fourth round at Wimbledon on 14 occasions, a performance only beaten in men's singles by Roger Federer (18) and Jimmy Connors (16).
"I thought I started off very, very well, very strong with a lot of good intensity, good focus," Djokovic said in an on-court interview.
"Honestly, I think I've been playing better and better as the tournament progresses, so that's something you wish for as a player, that every match you play you raise a level of tennis up a notch, at least, and I think that's what is happening at the moment.
"I know I can always do better, I always expect the highest from myself, and so far, so good, and I'm looking forward to the next challenge."