Djokovic, who won the event in his last appearance here in 2007, would meet Borna Coric in the second round.
Two wins would guarantee Djokovic the year-end No. 1 spot for a sixth season, matching the record set by Pete Sampras in the 1990s.
Coric, who lost the St. Petersburg final to Rublev last week, defeated Taylor Fritz 6-4, 6-4 after the American had 12 aces but dropped his serve at 4-4 in both sets.
The 153rd-ranked Austrian wild-card entry Jurij Rodionov upset Denis Shapovalov 6-4, 7-5 after the eight-seeded Canadian double-faulted 10 times.
Also, Kevin Anderson saved three match points in a third-set tiebreaker to overcome another Austrian player, Dennis Novak.
Anderson, who won the event in 2018, closed out a 6-7 (2), 6-4, 7-6 (6) win and next plays Pablo Carreno Busta, who led Gael Monfils 6-1, 2-0 when the seventh-seeded Frenchman quit the match with an injury.
Kei Nishikori pulled out with a shoulder injury on Monday evening, less than 24 hours before he was scheduled to take on defending champion Dominic Thiem.
Diego Schwartzman and Alex De Minaur also withdrew from the event, a day after losing the finals in Cologne and Antwerp, respectively.