Djokovic tested but prevails in Banja Luka opener against Van Assche
The world number one squandered three set points in the opener before Van Assche took the tie-break, but Djokovic broke twice in the second set to force a deciding set.
He dropped serve right away to start the third set but then broke Van Assche twice in a row, with Djokovic grasping control to eventually put away his 18-year-old opponent.
"It wasn't easy. This probably will rank as the slowest court and slowest conditions I've ever played in. I didn't expect this to be so slow," said Djokovic.
"I couldn't put any ball past him. He was on every single ball for a set and a half until I started to get some rhythm going and some tempo."
He added: "I'm happy with the way I finished the match. Of course I can always play better but a win is a win."
Former French Open junior champion Van Assche, the youngest player in the world's top 100 at number 87, had served Djokovic ample warning of his potential by beating Stan Wawrinka in round one.
Djokovic said Monday his elbow was not in "ideal condition" following a third-round exit last week at the Monte Carlo Masters, during which he was broken eight times by Lorenzo Musetti.
Van Assche earned the first break of the match for a 5-4 lead but failed to serve out for the set. He then saved three set points at 5-6 before eventually taking a surprise lead.
For the second set Djokovic disposed of the black compression sleeve on his right arm he also wore in Monaco, sweeping through without offering Van Assche a single break opportunity.
Despite falling behind to begin the third set, Djokovic recovered swiftly and sealed victory after two hours and 38 minutes.
The Serb, who is bidding for a record 23rd men's Grand Slam title at the French Open next month, will play countryman Dusan Lajovic or Gregoire Barrere of France in the quarter-finals.
