A dazzling exchange of passes with Neymar led to the second before Luis Suarez teed up the third in the second half. The Argentinian completed his sixth Champions League hat-trick in the process.
"The first goal is to win the group".
Celtic's attentions on the continent will turn next to their home game with City at the end of the month, where Rodgers will seek a notable upturn after a night to forget in Catalonia.
In his pre-match news conference Rodgers had waxed lyrical about Suarez, whom he bossed at Liverpool.
The result surpassed Barcelona's biggest win in the competition - a 7-1 victory over Bayer Leverkusen in 2012.
The two sides are familiar to each other as they have met on numerous occasions in the same tournament.They have been playing each other more often in the last four years in Champions league football.
Dembele was Celtic's hat-trick hero in a 5-1 thrashing of Glasgow rivals Rangers on Saturday, but he failed to add to his burgeoning reputation as ter Stegen flew to his right to turn the Frenchman's penalty behind.
Joshua Kimmich grabbed a second-half double, with Robert Lewandowski scoring from the penalty spot, birthday boy Thomas Mueller and Spanish defender Juan Bernat giving Bayern early custody of Group D. We are at a big club and we want to win games.
In a rematch of a Round-of-16 encounter last season, Atletico Madrid beat PSV Eindhoven 1-0 in the Netherlands. It was easier after the first goal.