The Croatian had lost his previous four matches but triumphed in two hours 48 minutes to set up a meeting with Jan-Lennard Struff.
American Taylor Fritz made it through qualifying for the first time this season and upset Grigor Dimitrov 7-6(8) 7-6(4) to set up a second round showdown with world number one Novak Djokovic.
"It's a pleasure to be back here," Djokovic told reporters on Monday.
"I've had very good successes and some good results here in the past. And I'm happy to be healthy playing here.
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"Maybe I haven't been at my best level in the last two months but bit by bit we're getting that back and I hope my best tennis comes out here."
Russia's Karen Khachanov beat Jaume Munar 6-4 6-7(5) 6-3, while Gael Monfils breezed past Andreas Seppi 6-3 6-1.
(Reporting by Rik Sharma, editing by Pritha Sarkar)
