In a tight opener, the Serb managed to save four set points, before converting one of his own on the third attempt in a tiebreak which ended 13-11.
Djokovic then broke serve early and held his own throughout before breaking again to take the match and set up a tie against the winner between Hubert Hurkacz of Poland and Italian lucky loser Lorenzo Sonego.
In first round action in Vienna, third seeded Greek Stefanos Tsitsipas saw off Germany’s Jan-Lennard Struff 6-7 (3) 6-3 6-4 in just under two hours, while fourth seed Daniil Medvedev of Russia eased past Jason Jung, another lucky loser, 6-3 6-1.
Medvedev will next face Vasek Pospisil, who beat Felix Auger-Aliassime 7-5 7-5 in an all-Canadian encounter.