Bayern again came close after 18 minutes with an effort from David Alaba, but his effort from 16 yards missed the target.
It was the home side who continued to dominate in the opening period and Kroos came close with an effort after 35 minutes, but Basel continued to resist the second goal.
Bayern opened up a comprehensive lead before the break, however, as Thomas Muller added a second after 42 minutes, before Gomez tapped over the line just before the break.
Bayern wrapped up the tie after 50 minutes when Gomez added his second of the night after good work from Franck Ribery.
It was five, and quickly six for the German side just past the hour mark when Gomez scored his third and fourth of the night after a double assist from Ribery.
Bayern rounded off an extremely impressive night with a seventh late on courtesy of Robben.
The draw for the latter stages of the Champions League will be made on Friday.