The Gunners found themselves two goals behind in the opening 15 minutes in Sofia, but goals from Granit Xhaka and Olivier Giroud had them level at the break.
The second half did not produce as much entertainment until Mesut Ozil was played in by substitute Mohamed Elneny with three minutes remaining and showed great composure to slot home and secure a 3-2 victory.
With group A rivals Paris St Germain winning in Basle, the pair are already assured of qualification to the knockout stages of the Champions League - with their meeting at the Emirates Stadium later this month now essentially a play-off for top spot.
When asked if Arsenal's character had once again been tested, Wenger said: "I give credit to the team spirit for that. You get belief with positive results, and this shows a healthy mentality in the group. The two together come out in these kind of games.
"We were caught cold and were 2-0 down. After that, I felt we kept our composure, didn't panic and came slowly back. It was good to be 2-2 at half-time.
"We dropped a bit physically in the second half, but continued to dominate even if we were exposed to counter-attacks."