With 61 minutes on the clock, Slovan Bratislava's Kevin Wimmer found the net following a Marko Tolić assist to pull one back for Slovan Bratislava.
Celtic's Daizen Maeda also increased the lead for Celtic in the 70th minute, with an assist by Reo Hatate.
The 5-1 goal came, when Adam Idah found the net for Celtic, with an assist by James Forrest.
Celtic play Borussia Dortmund on 1 October, Atalanta on 23 October and RB Leipzig (home) on 5 November. Slovan Bratislava's next opponents are Manchester City on 1 October, Girona on 22 October and Dinamo Zagreb (home) on 5 November.
Ahead of Wednesday's game, Slovan Bratislava had enjoyed a run of eight games without defeat.
Celtic emerged triumphant over Slovan Bratislava in Wednesday's Champions League clash at their home ground. Despite an early lead of 1-0, Celtic demonstrated strength and composure, extending their lead to secure a 5-1 victory.
In the 56th minute, Arne Engels increased the lead for Celtic.
For the home team, the results mean second place in the table. Slovan Bratislava are in 26th place.
Celtic started the match well and took the lead early when Liam Scales netted in the 17th minute, with an assist by Arne Engels, making it 1-0.
Straight after the break, Kyogo Furuhashi found the net and increased the team's lead.