The Ukrainian defender scored the only goal at the Parc des Princes in the 39th minute, helping Luis Enrique's side secure three important points and maintain their position at the top of the French league.
PSG created several opportunities early in the encounter, with Senny Mayulu coming close to scoring when his effort struck the woodwork in the opening five minutes.
Troyes goalkeeper Hillel Konaté also produced important saves to deny Mayulu and Ferran Torres as the hosts dominated possession.
The breakthrough eventually arrived from a corner. Désiré Doué played the ball to Mayulu, whose delivery into the penalty area was met by Zabarnyi, who directed a powerful header beyond Konaté.
The goal was Zabarnyi's first in all competitions this season.
PSG unable to extend their advantage
PSG continued to control proceedings after the interval but struggled to convert their chances into additional goals.
Mayulu and Warren Zaïre-Emery both threatened, while Torres was denied by Konaté as the visitors worked hard to remain in the contest.
Troyes also had opportunities to equalise. Renaud Ripart failed to take advantage of a promising opening, while a late effort from Lucas Maronnier was ruled out for offside.
Despite the pressure, PSG maintained their defensive discipline to secure a clean sheet and another league victory.
PSG extend winning streak
The result marked PSG's 11th consecutive victory across all competitions and strengthened their position at the top of Ligue 1.
The defending champions moved to 23 points, three ahead of second-placed Paris FC, who also secured a victory against Auxerre.
Troyes remained 16th with eight points after their defeat in the French capital.
PSG will now turn their attention to their next league assignment against Nice on 21 November, following the international break.
Match details
• Competition: French Ligue 1, Matchday 10
• Venue: Parc des Princes, Paris
• Full-time: Paris Saint-Germain 1-0 Troyes
• Goal: Illia Zabarnyi 39'
• Assist: Senny Mayulu
• Player of the Match: Illia Zabarnyi