This was Bayern's fifth win of their European campaign and Louis van Gaal's side progress to the knock-out stages alongside AS Roma while Basel finish third with the consolation of a place in the Europa League.
"Not many sides have managed to win five of their group games," beamed van Gaal. "We scored three goals, so I am very happy. This win will also give us some self-confidence for the games ahead."
A pair of goals from Ribery - his first for the club since April - and a simple tap in by Ukraine star Anatoliy Tymoshchuk, who is enjoying a purple patch, sealed the win in Munich. But all is not rosy with the German champions.
Tougher tests await in February's round of 16 which will be drawn on December 17 in Nyon and captain Mark van Bommel was not impressed.
"We started this game badly, there was not enough movement and calls for the ball until Franck opened the scoring," said the Dutchman. "We should have scored more goals, it is important to take some confidence for our (next Bundesliga) match against St. Pauli."
There are already real concerns around the Allianz Arena about qualifying for next season's competition and Bayern need to finish in the German league's top two to be sure of a place in European football's most lucrative tournament.
Their 2-0 defeat at German league strugglers Schalke on Saturday leaves them seventh in the Bundesliga and 17 points behind surprise leaders Dortmund with van Gaal already admitting the gap may be too big to bridge.
The Germans have now won their last seven European home games, but there is no denying they are erratic on occasion and have lost four times in the Bundesliga this season.
The last time the two sides met in September, Bayern won 2-1 thanks to a late Bastian Schweinsteiger goal and the hosts took a 2-0 lead in as many minutes here.
Bayern scored when defender Diego Contento won the ball on the edge of the penalty area and squared to Ribery who slammed home his shot on 35 minutes.
The Germans struck again moments later when Mario Gomez rose highest at a corner and headed down for defensive midfielder Tymoshchuk to stab the ball home.
The hosts made sure of the victory just five minutes into the second-half when Thomas Müller found acres of space down the right flank and squared for Ribery to net his second of the night.
But Basel should have at least scored a consolation goal when Bayern defender Breno was robbed of possession by Swiss striker Alexandra Frei who squared the ball back inside but forward partner Federico Almerares fired over.
Bayern are set to welcome back long-term injury victims Dutch playmaker Arjen Robben, Croatia striker Ivica Olic and Germany veteran Miroslav Klose in January.
The Germans will need all the firepower they can muster if they are to repeat last season's feat of reaching the final.