The German giants scored three times in the second half in a relentless performance which sees them firm favourites to progress to the decider to be held at London's Wembley Stadium on May 25.
There was a hint of offside as Muller's glancing header from a corner found its way deep into the box before Gomez volleyed home from close range.
In the 73rd minute, it was 3-0 as Arjen Robben dazzled Jordi Alba on the right side of the area before cleverly slotting through the legs of Valdes although Muller could have been pulled up for a body check on Alba as he looked to defend.
Nonetheless, the goal stood and Bayern then took complete control when adding a fourth in the 82nd minute through Muller who flicked in David Alaba's cut back from the left.
Jupp Heynckes' side cut Barcelona to ribbons on occasions in a powerful effort at home and will now need to hold their nerve in defence as Tito Vilanova's Barca will certainly be looking to produce an all-out attacking performance at the Camp Nou in the return bout on May 1.
2012/13 UEFA Champions League semi-final - first leg
Allianz Arena, Munich - 68,000