The 33-year-old Serbian star made his feelings clear after he was broken when serving for victory in the second set.
"How much do you wanna play?" Djokovic yelled at umpire Nacho Forcadell. "I asked you three times; you are not checking anything."
The match was eventually suspended for three hours before Djokovic secured a 6-3 7-6 (5) victory.
Djokovic said he had been struggling with the court conditions before the players were sent off the court at 5-5 in the second set.
"It was a very strange match with strange conditions,'' Djokovic said. "Obviously, playing under the rain nonstop for almost two full sets, it is challenging for both me and him.
"I thought that I had an advantage there because the conditions were slower which allows me to return his serves, because he's got really big serves," Djokovic continued. "So I kind of kept the match under my control for most part of the two sets, then served for the match. Very sloppy service game. He played well, made a great passing shot to come back."
Djokovic was disqualified from last year's US Open after accidentally hitting a line judge with a ball during his fourth-round match against Spain's Pablo Carreno Busta.
American player Reilly Opelka, who is playing in this week's tournament after a bout with COVID-19 that kept him off the court entirely for more than two weeks and prevented him from practicing the way he usually does for nearly a month, won his second straight match -- beating Lorenzo Musetti of Italy 6-4, 6-4 to reach the round of 16.
Next up for Opelka at a tournament many players use to prepare for the French Open, which begins May 30, will be either second-ranked Daniil Medvedev or No. 27 Aslan Karatsev, whose match was among those postponed by the weather Tuesday.
Earlier, ninth-seeded Matteo Berrettini rallied to beat Nikoloz Basilashvili 4-6, 6-2, 6-4 -- less than 48 hours after losing the final in Madrid. Fellow Italian Lorenzo Sonego is also through to the second round after celebrating his birthday by beating 14th-seeded Gael Monfils 6-4 5-7 6-4.
Kei Nishikori was handed a walkover in his second-round match against 11th-seeded Pablo Carreno Busta. Eighth-seeded Diego Schwartzman was beaten 6-1 6-3 by Canadian Felix Auger-Aliassime, who moves into the third round.
In the women's bracket, Madison Keys defeated Sloane Stephens 6-4, 2-6, 7-5 in an all-American matchup. Three seeded players were upset -- No. 10 Belinda Bencic (6-3, 6-4 by Kristina Mladenovic), No. 14 Elise Mertens (4-6, 6-2, 6-3 by Veronika Kudermetova) and No. 16 Johanna Konta (3-6, 1-6 by Jelena Ostapenko).
Reuters and The Associated Press contributed to this report.