Arjen Robben scored the opener before Thomas Müller bagged the second goal of the game in the 42nd minute to put Bayern ahead on aggregate after Basel’s surprise 1-0 win in the first leg.
German international striker Gomez netted his first of the night two minutes later, just reward for Munich’s sizzling first-half performance at the Allianz Arena.
If Basel’s hopes were fast fading, they were crushed in style in the second half when Gomez added three more goals to his tally by the 67th minute.
Robben added the final flourish in the 81st as Bayern kept alive their dream of winning Europe’s top trophy at their home ground.