WATCH the ATP Tour LIVE on beIN SPORTS | available via Foxtel, Kayo Sports, Fetch TV & beIN SPORTS CONNECT
Moraing, who is ranked 252 places below Djokovic, beat Egor Gerasimov 4-6 7-6 (9-7) 7-5 in a gruelling encounter on Monday.
Djokovic is seeking his 83rd Tour-level title as he warms up for the French Open, the main draw of which begins on May 30.
Fellow home favourite Dusan Lajovic, the highest seed to compete on day one, will meet Jeremy Chardy next after beating Ricardas Berankis in straight sets.
Eighth seed Federico Delbonis required three sets to see off Lukas Klein, while seventh seed Miomir Kecmanovic – another Serbian in the draw – was beaten 6-3 6-2 by Pablo Cuevas.
Veteran Fernando Verdasco set up a contest with Adrian Mannarino after an impressive 7-5 6-2 win over Lucas Pouille.
At the Emilia-Romagna Open in Parma, all of Monday's play had to be cancelled due to persistent rain.
Fifth seed Richard Gasquet is in action on Tuesday.