Bayern came into the match following a home defeat against Cologne in the Bundesliga, but were a team transformed here, scoring goals from almost all of their chances.
"The result is positive for us as it opens the road to the quarter-finals," Bayern manager Jurgen Klinnsmann said.
"It is positive, especially since the last games did not go that well for us, but we cannot become overly enthusiastic and must prepare calmly for the match on Sunday against Werder Bremen," he added.
Sporting made history by reaching the knockout rounds for the first time, but will not recall this baptism fondly.
"The feeling is one of frustration. It's not normal to lose with this type of result in this phase of the Champions League" said Sporting manager Paulo Bento.
He added that Sporting had been the better team in the first half, but became "disorganised in the second half and let the more experienced and mature Bayern take control of the game".
The Portuguese team created the first chance of the match after 11 minutes with Anderson Polga's shot cleared off the line by Martin Demichelis, but Bayern responded moments later with Ribery shooting wide.
The Frenchman did not waste his next chance, stealing the ball in Bayern's half, beating three defenders and scoring from inside the Sporting box on 42 minutes.
Sporting were unable to put Bayern under pressure at the start of the second half, and Miroslav Klose doubled the lead on 57 minutes from an assist by Luca Toni.
Ribery scored his second goal on 63 minutes, converting a penalty after a foul by Fabio Rochemback on Philipp Lahm, and and was also involved in Bayern's fourth, crossing from the left wing for Toni to head in.
The Italian completed the scoring in the 90th minute from close range after some poor defending by Sporting.
