The Socceroos winger teed up Sander van de Streek 10 minutes from time to cap off a fine 45-minute cameo and send the Domstedelingen into the second round.
Bart Ramselaar had given Utrecht an early lead at the GN Bouw Stadion and soon doubled his tally after Nikolas Agrafiotis restored parity for the second-tier side.
Though Agrafiotis, too, would later secure his second, it wasn't before Gyrano Kerk helped Utrecht to their third goal of the contest.
Arzani's introduction came in place of Kerk at the start of the second half, and the 21-year-old found van de Streek with his second assist of the 2020-21 campaign.
Utrecht have now won back-to-back matches across all competitions and will look to build on their bright start against Heracles on Sunday (AEDT).
