It was the biggest win in a Champions League knockout match as records tumbled in Munich and Bayern bettered their 7-1 home win over Sporting Lisbon from the 2009 competition, also in the round of 16.
Having come to Germany holding a 1-0 lead from the first leg three weeks ago, Basel's dreams of reaching the Champions League's last eight for the first time were rudely awakened as they lost the tie 7-1 on aggregate.
Bayern coach Jupp Heynckes hailed his team's 'perfect' performance as they have now scored 14 goals in their last two games.
"We had already played well last Saturday and I noticed this week how much the team wanted to go through to the next round," he said after his team also smashed Hoffenheim 7-1 last Saturday in the German league.
"Today, we have put in a top class performance from the first until the last minute. Overall, it was a perfect game from us."
It was also Basel's worst ever away European defeat, breaking the 5-0 record set in 1963 at Celtic and equalled in 2008 at Shakhtar Donetsk in Ukraine.
Munich's Allianz Arena hosts the final here on May 19 and the Bavarians strolled into Friday's quarter-final draw at UEFA headquarters in Nyon.
Having netted a hat-trick against Hoffenheim, Gomez scored four more, while Dutch winger Arjen Robben again scored twice against Basel.
"It was fun to play in that. To score seven goals in a Champions League match speaks for itself," said Robben. "We have to stay focused. It would be good to get Barcelona or Real Madrid in the next round, but we'll take whoever comes."
Basel ended Manchester United's involvement in this season's campaign in the group stage, but spent the majority of the match defending and were totally outplayed.
"You have to see this is a game to try to take something positive away from," said Basel coach Heiko Vogel. "Maybe we can learn more from this than the wins we've enjoyed so far in the competition."
"Of course you have to talk about the quality Bayern have, but we need to learn our lessons."
Heynckes stuck with the same team that hammered Hoffenheim and they were 3-0 up at the break.
Robben opened the scoring on 11 minutes when he played a pass into Toni Kroos, whose shot clipped a Basel defender's boot and fell into Robben's path to blast home from 12 yards.
It was all Bayern as Basel won only their first corner with 34 minutes gone and any threat was comfortably dealt with by Munich goalkeeper Manuel Neuer.
Mueller made it 2-0 on 42 minutes when he converted a Robben cross and found enough space at the near post to beat Yann Sommer on the volley.
The third came less than two minutes later as defender Holger Badstuber squared the ball from a free-kick and with Gomez and Luiz Gustavo queueing up to score, it was Gomez who got his boot to it.
Gomez added his second on 50 minutes when he turned in a Franck Ribery cross and in an almost carbon copy of the fourth goal, Gomez completed his hat-trick when he latched onto a Ribery cross and headed home on 61 minutes.
Gomez netted his third after the break on 67 minutes when he slotted home yet another cross from Ribery, who was untroubled down the left flank.
By this stage the Basel defence had been cut to ribbons and Robben added more salt to their wounded pride by rounding Sommer to slot home Bayern's seventh and his second of the night on 81 minutes.