Coming off his 89th career title in Tel Aviv last weekend, Djokovic broke an overmatched Garin five times to continue his push for a place in the season-ending ATP Finals.
"From the start to the end, [it was] a great performance," said Djokovic. "Playing in a new tournament, different conditions, the first match is never easy. Obviously you are looking to see how you are going to adapt, but I did it perfectly, really, played as well as I can."
The Serb is the only player to win ATP tournaments on clay, grass and hard courts this year. He will play Dutchman Botic van de Zandschulp for a place in the quarter-finals.
"Coming into this tournament I feel confident, I feel excited, I feel motivated, so I think that helps as well to adjust quickly," added Djokovic.
Third seed Stefanos Tsitsipas ended the run of Italian qualifier Luca Nardi, advancing 7-6 (7/2), 7-6 (7/3). He goes on to face Kazakhstan's Alexander Bublik or Hubert Hurkacz.
Andrey Rublev, seeded fifth, defeated China's Zhang Zhizhen 6-3, 6-2 in his second round match.
Rublev meets Adrian Mannarino next after the Frenchman put out David Goffin, who shocked world number one Carlos Alcaraz in the opening round.
Roberto Bautista Agut beat lucky loser Pavel Kotov 6-1, 7-6 (7/5) and could play Daniil Medvedev in the quarter-finals.
Marin Cilic, the runner-up to Djokovic in Tel Aviv, won his opener 5-7, 7-6 (7/4), 6-2 against Germany's Oscar Otte.
Switzerland's Marc-Andrea Huesler, who won his first ATP title in Sofia last week, was dumped out by Emil Ruusuvuori 6-0, 6-2.
