Mbappe netted twice in seven minutes before Messi bagged a brace of his own against the Belgians on Tuesday night.
Messi's double took him past Pele's all-time total of 757 career goals, with the Argentine now second behind Cristiano Ronaldo's 801.
Mbappe, meanwhile, took his Champions League tally to 31, making him the youngest ever player in the history of the competition to achieve that feat.
The French superstar is aged 22 years and 352 days and not only could he one day surpass Messi and Ronaldo, has already gone past two legends of the competition.
Manchester United icon Wayne Rooney and former Barcelona and Inter Milan forward Samuel Eto'o were both above Mbappe before the start of play but have now been overtaken by the PSG man.
Messi, though, won't let Mbappe chase down his tally anytime soon and he netted a trademark left-footed finish and a penalty to extend his Champions League tally to 125 goals.
Club Brugge had improved in the second half and netted a consolation through Mats Rits but were never going to be a match for the Parisians and finished bottom of their group.
Messi is still well behind Man United legend Ronaldo in both the all-time charts and the Champions League.
The Portugal captain is 36-years old but is showing no signs of slowing down and is currently clear of Messi on 140 goals in the competition.
Mbappe, meanwhile, is still widely expected to join Real Madrid next summer upon the expiration of his contract and can start negotiating with Los Blancos in January.
The club were in fact so keen to secure his services this season, they submitted a mammoth €220million (around £187m) offer on deadline day for the PSG forward.