The Gunners made an impressive start at the Eden Arena on Wednesday, taking the lead after nine minutes when Gyökeres produced an excellent through ball for Madueke, who finished to put the visitors ahead.
Arsenal continued to dominate and doubled their advantage in the 38th minute. Mikel Merino played Gyökeres through on goal and the Swedish striker kept his composure to beat the goalkeeper with a well-taken finish.
Mikel Arteta's side looked firmly in control at half-time, but the match changed significantly after the interval as Slavia increased their intensity and began creating opportunities.
Wiktor Nowak pulled a goal back in the 90th minute, converting David Jurásek's cross to set up a tense finish. Arsenal were forced to defend their advantage, with David Raya making important saves and Gabriel Magalhães clearing a dangerous header off the line.
Arteta admitted that his team had fallen well below their standards after the break.
"First of all, you have to value the fact it's very difficult to win away from home. We've done it against a very tough opponent, we expected that toughness. Two very different halves - the first we played at a really high level in terms of intensity, tempo, quality and clarity in what we had to do, and what the game was demanding. We were very efficient - we should have scored three, four or five," he said.
"We didn't make that gap, and at half-time, the message was clear. There was still a lot to do in the game - this was a team we were up against with huge spirit, and if you give them something, they will grab it."
The Arsenal manager accepted responsibility for the deterioration in his team's performance.
"Right from the beginning of the half, we were extremely far from our standards, the basics, the concepts, and everything we discussed to avoid. It was far from what we expect from each other, but we found a way to hold onto the result and win the game."
Arteta was particularly pleased with Gyökeres, who delivered a goal and an assist.
"I thought he was really good. It was a game we believed would be really good for him, for the demands the opponent puts in and the spaces he could use. He's done it really well, not just for the assist and the goal, but he was really connected to the team. It's really great news for him, because he really needed that performance."
Slavia coach Jindřich Trpišovský felt his side had responded well after a difficult opening period.
"At half-time, we had a long and honest discussion. The substitutions worked well, and the change in formation made a difference. We started the second half strongly. In the first half, we were too far away from our opponents and Arsenal had a clear edge. They gave us a footballing lesson, but after the break we got much closer to them. We fought for every ball, competed hard and played with real intensity."
Trpišovský added that the second half offered valuable lessons for his team, while expressing satisfaction that they had given their supporters something to celebrate through Nowak's late goal.
Arsenal secured their third victory in four Champions League matches, taking their points tally to 10 and moving into third place in the league-phase standings.