The Gunners produced a strong first-half performance to establish a two-goal advantage, with Noni Madueke and Viktor Gyökeres finding the back of the net to put Mikel Arteta's side in control of the encounter.
The result also lifted Arsenal to third place in the Champions League table, further strengthening their position in the competition.
However, the Premier League champions were unable to build on their early advantage, allowing Slavia Prague to remain in contention as the match progressed.
Wiktor Nowak's late strike reduced the deficit and set up a nervy finish, forcing Arsenal to defend their lead during five minutes of added time.
Slavia continued to push forward in search of an equaliser, but Arsenal showed defensive resilience to withstand the late pressure and preserve their advantage until the final whistle.
Beyond securing all three points, the victory marked a historic achievement for the North London club, whose unbeaten away streak in the Champions League has now reached 10 matches for the first time in their history.