Celtic placed down an early Champions League marker after hammering Slovan Bratislava 5-1 in Wednesday's opener. (More Football News)
Arne Engels teed up Liam Scales' fierce headed opener in the 17th minute at Celtic Park, before the midfielder himself scored from the penalty spot in the second half.
Kyogo Furuhashi had earlier added Celtic's second goal of the game just nine minutes before Engels' penalty, awarded for a needless pull on Alistair Johnson by Danylo Ignatenko.
Switzerland defender Kevin Wimmer reduced the arrears on the hour with a delightful outside-of-the-boot finish, though Daizen Maeda soon restored the advantage 10 minutes later after linking up with Reo Hatate.
Substitute Adam Idah rounded the scoring off with four minutes remaining, latching onto James Forrest's pass to complete a convincing triumph.
Data Debrief: Celtic firing on all cylinders
Engels' fine individual showing made him only the second player to both score and assist a goal on his Champions League debut for Celtic, after Sweden great Henrik Larsson against Juventus in September 2001.
Brendan Rodgers' side were completely dominant in every aspect, too, accumulating a massive 3.22 expected goals (xG) tally to Bratislava's minimal 0.30.
It was also just the second time Celtic have smashed four or more goals in one match in the competition, having also managed to do so in a 4-3 victory over Juve in October 2001.
With goals coming from all over the place, Celtic had five different scorers in a European Cup/Champions League match (excluding own goals) for the first time since September 1973 against TPS Turku (Dixie Deans, George Connelly, Harry Hood, James Johnstone, Thomas Callaghan).