The victory also saw the Gunners move up to third in the table.
The Premier League champions raced into a two-goal lead in the first half, thanks to Noni Madueke and Viktor Gyökeres.
However, Arsenal failed to add more goals and Wiktor Nowak’s late strike set up a tense finish.
The goal set up five minutes of stoppage time, during which Slavia continued searching for an equaliser, but Mikel Arteta’s men held on to secure all three points.