Djokovic, the 2011 champion, carved out a 6-4, 6-3, 6-7 (5/7), 7-6 (7/5) victory over the 35-year-old Czech who has now lost 11 of the pair’s 12 meetings.
But the world number two progressed the hard way, squandering a 5-2 lead in the third set tie-break before recovering his composure.
Confident statistics of 18 aces and 54 winners helped lay the foundation for victory and a third round clash with French world number 44 Gilles Simon.
“I should have closed it out in the third set. I had some break point chances and the lead in the tie-break, so I should not have complicated my life in this way, but credit to him,” Djokovic said.
Defending champion Andy Murray handed out a tough Wimbledon lesson to Slovenia’s Blaz Rola, a former US college champion, coasting to a 6-1, 6-1, 6-0 win over a grasscourt rookie playing just the 10th match of his career.
The British third seed eased to victory in just 84 minutes, hitting seven aces and 27 winners against the world number 92 and goes on to face Spanish 27th seed Roberto Bautista Agut.
“It’s his first year on grass so it was tough for him. But he has a good game and he’ll keep improving,” said Murray.
“I took care of my serve for the majority of the match and I played well. If you can finish matches as quick as possible then that’s better in the long run.”
Spanish seventh seed David Ferrer failed in his bid to reach an 18th consecutive third round at a Grand Slam when he was knocked out by Russian qualifier Andrey Kuznetsov.
The 32-year-old Ferrer last failed to reach the third round at a major at the 2010 Australian Open, but Kuznetsov, the world number 118, claimed a famous 6-7 (5/7), 6-0, 3-6, 6-3, 6-2 win to reach the third round for the first time.
Ferrer had come into the tournament still suffering the after-effects of the stomach illness which forced him out of the ‘s-Hertogenbosch grasscourt warm-up in the Netherlands last week.
“It’s a disappointment, but it’s not the end of the world,” said the Spaniard.