The Dutch winger looked to have beaten Alba, but his case was quite clearly helped by Muller bundling the defender to the ground.
While the visiting team stopped in anticipation of the referee's whistle, Robben continued his run and lashed the ball into the far corner before turning away to celebrate.
Quite how the foul was missed by the referee and the extra officials behind the goal is extraordinary, but that scarcely mattered to a rampant Bayern.
Muller almost added a fourth when he raced clear only to be denied by a fine block by Valdes as Barcelona began to crumble.
Bayern's surpremacy was emphasized further two minutes later when David Alaba rampaged down the left and picked out Muller to flick the ball home.
"I think we knew we were able to give them good competition," Robben told ITV following his side's impressive showing.
"I think everybody said before it was a 50-50 game.
"We can be very proud, this team (Barcelona) has dominated Europe over the last five years and if you beat them like this in such terrific way I think you can be proud.
"But on the other hand, let's be quiet, enjoy this evening but not anymore, because there's still the second game to play and we have to be ready."
Barcelona now faces an "almost impossible" task to make the final and defender Pique admits his team was completely outplayed.
He told television channel TV3: "There's not much you can say, they've been faster, stronger and played the better football.
"We mustn't talk about the referee; I don't think he had any influence.
"It's almost impossible for us. They've been better than us, we need to congratulate them and show our best in the return leg, while thinking about finishing the league as soon as possible.
"We are Barca. We must go out at the Nou Camp to win the game for our fans."