Bayern, who won the first leg in Lisbon 5-0 two weeks ago, raced to a 4-1 halftime lead helped by two goals from Germany striker Lukas Podolski and an own goal before adding three more in the second half.
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Bayern's aggregate win beat the competition record 10-2 margin set by Olympique Lyon against Werder Bremen in the 2004-05 season and they also became the first team to score 12 goals in a two-legged Champions League knockout tie.
They also equalled the biggest winning scoreline in one leg of a knockout round tie in the competition.
Bayern coach Jurgen Klinsmann, who has been under fire for the team's inconsistent league showing, said Bayern were hungry for more success in Europe.
"We wanted to show from the first second who was boss," Klinsmann said. "Sporting saw early on there was nothing to gain and then came the fun and the flow. My players had fun. Now we are hungry and we want to go far."
Playing with no pressure despite missing several key players through injury, including playmaker Franck Ribery and top striker Luca Toni, Bayern grabbed the lead after only eight minutes through Podolski's powerful left foot from 18 metres.
Podolski, who will be leaving at the end of the season for Bundesliga rivals Cologne, added a second after 34 minutes when keeper Rui collided with defender Anderson Polga allowing the Bayern striker to score with a bicycle kick from 10 metres.
MORE MISERY
There was more misery to come for Sporting, who by now were in complete disarray, when Polga volleyed a Bayern corner into his own goal six minutes before the break before captain Joao Moutinho's well-struck long-range effort salvaged some pride.
But a minute later, in the 43rd, Bastian Schweinsteiger restored the three-goal margin when defender Christian Lell raced down the right wing and cut back into the box for the midfielder who had no trouble firing home.
With most of the team attacking, it was captain Mark van Bommel's turn to score Bayern's fifth when he had time to control the ball in the box and fire home after 74 minutes.
Striker Miroslav Klose finally made the scoresheet, netting his seventh Champions League goal of the season, with an 82nd-minute penalty he himself won after racing into the box before being clipped by Pedro Silva.
Teenage substitute Thomas Mueller, who had set up Bayern's fifth, netted the seventh with a tap-in a minute from time after yet another defensive blunder.
"When our first chances went in then it became easy, the ball is flowing and you can play like we played today," van Bommel said.
"But we must remain down to earth. Let's hope we get a good draw in the next round."
