Tzolis showed Arsenal fans a glimpse of what may be to come as he scored on his first Gunners appearance in their opening pre-season win over Girona.
Signed to replace Leandro Trossard after his transfer to Besiktas, the Greece international made the switch to north London in a £34m transfer from Belgian side Club Brugge.
Tzolis, 24, skipped beyond Arnau Martinez before firing a low effort into the bottom of the net via the help of a slight deflection in the 30th minute.
But it was German forward Kai Havertz who slotted Arteta’s side into the lead 14 minutes earlier.
Sixteen-year-old Max Dowman threaded a fine pass through for Havertz to calmly finish when one-on-one with Girona goalkeeper Paulo Gazzaniga.
Four minutes after the break, Martinez climbed highest from the Girona corner to halve the deficit before Dowman reinstated Arsenal’s two-goal lead three minutes later.
The flurry of goals was not over there as Gabriel Jesus made it three goals in five minutes to fire the Gunners into a 4-1 lead.
Arteta named a strong starting XI in Spain with Viktor Gyokeres, Havertz and Hincapie each playing 30 minutes after their return from the World Cup.
Arsenal will travel to Dublin for their second pre-season game when they take on Real Betis at the Aviva Stadium on 5 August.