The Gunners made a bright start and took the lead in the ninth minute through Noni Madueke, who finished confidently after Viktor Gyökeres supplied an excellent pass to put him through on goal.
Arsenal continued to control proceedings and doubled their advantage in the 38th minute. Gyökeres got on the scoresheet himself, finishing superbly after combining with Mikel Merino to give the visitors a comfortable half-time lead.
However, the contest changed after the break as Slavia Prague increased their attacking intensity and put the Arsenal defence under sustained pressure.
The Czech side created several opportunities, forcing goalkeeper David Raya into important saves. Gabriel Magalhães also produced a crucial goal-line intervention to preserve Arsenal’s advantage.
Slavia eventually found a breakthrough in the 90th minute when Wiktor Nowak scored from close range following a cross from David Jurásek.
The late goal set up a tense finish, but Arsenal held on to claim all three points and avoid surrendering their two-goal advantage.
The result gave Arsenal their third victory in four Champions League league-phase matches, strengthening their position in the race for automatic qualification to the knockout stage.
Arteta will nevertheless be concerned by his team's second-half performance, particularly after Slavia registered 18 shots compared with Arsenal's 12.
Full-time: Slavia Prague 1-2 Arsenal
Goalscorers:
• Slavia Prague: Wiktor Nowak 90'
• Arsenal: Noni Madueke 9', Viktor Gyökeres 38'
Arsenal will now turn their attention to their next fixture against Hull City on Saturday before continuing their Champions League campaign.