Djokovic, who had not played in Madrid since 2013, served four double faults but relied on his return to overpower Coric.
“I thought I was serving quite well in the practice sessions, but then the first set went well, the second, not so much,” said Djokovic, who claimed his only Madrid title in 2011 when he beat Rafael Nadal in the final.
“The first serve percentage could have been higher and should be higher for the upcoming matches. But I’m satisfied with my game.”
Coric’s style has been compared to that of `a young Djokovic,’ and the Serb said his opponent had a “nice balance between confident approach and self-belief on the court, and is not really intimidated by anyone’s presence.”
Djokovic said he could “identify myself with him because we have very similar backgrounds, coming from Croatia and Serbia. We have the same mentality, speak the same language and more or the less same trajectory or path to professional tennis.”
Tennis fans are bound to see more of Coric, Djokovic predicted, adding: “And I’ll be glad to help him become better.”
Djokovic’s next opponent will be Roberto Bautista Agut.
Also, Nick Kyrgios of Australia put in a hard-hitting performance to beat fourth-seeded Stan Wawrinka of Swizterland 7-6 (7), 7-6 (2), while sixth-seeded Kei Nishikori advanced by beating Fabio Fognini 6-2, 3-6, 7-5.
In the women’s draw, fourth-seeded Victoria Azarenka pulled out of the tournament because of a lower back injury.
Azarenka had been scheduled to play Louisa Chirico of the United States on Wednesday, but she withdrew during the warmups.
Azarenka said “I don’t feel that I’m able to compete today,” adding she will undergo medical tests in Madrid later Wednesday before making a decision about playing in Rome.
She said it is going to be a matter of making the “smart decision.”