With several first-team regulars still on holiday following the World Cup, Mikel Arteta named a limited squad that nonetheless included Tzolis, who joined from Club Brugge in a £34m move and started on the left of a front three alongside Gabriel Jesus and Reiss Nelson.
It was Nelson who opened the scoring after 10 minutes, finding space inside the box before finishing coolly past MK Dons goalkeeper Craig MacGillivray, though the more eye-catching contribution came from Tzolis, who provided the assist.
The Greek international registered 29 assists for Club Brugge last season and looked to have picked up where he left off, already showing signs of an early understanding with Riccardo Calafiori down the left side that Arteta will hope translates into competitive fixtures once the season gets under way.
Ethan Nwaneri doubled Arsenal's lead just before half-time with a trademark finish, collecting the ball just outside the box before curling an effort beyond the MK Dons keeper. Arteta used the interval to introduce eight academy players, part of a squad now working under new academy director Pascal De Maesschalck, while goalkeeper Illan Meslier came on in the 59th minute alongside further young prospects including highly rated left-sided defender Marcel Washington.
It was another of the half-time substitutes, Ceadach O'Neill, who completed the scoring, running through on goal and finishing with composure to make it 3-0.
The comfortable win provided a useful first run-out for Arteta's side as they continue building towards the new season, with the squad set to be bolstered by returning World Cup participants before Arsenal face Girona in Spain on August 1, a fixture expected to give a clearer picture of Arteta's first-choice options ahead of the Premier League campaign.
Arsenal first half: Arrizabalaga, Copley, Mosquera, Salmon, Calafiori, Lewis-Skelly, Nwaneri, Nelson, Dowman, Tzolis, Jesus.
Arsenal second half: Arrizabalaga (Meslier 59), Ogunnaike, Salmon (Julienne 59), Clarke, Copley (Washington 59), Ibrahim, Agustien, O'Neill, Harriman-Annous, Kabia, Mooney.