Milan's defence will have to produce a repeat performance against Barca next Tuesday and hope for an away goal of their own if they are to progress and face either Chelsea or Benfica in the semi-finals - the English side lead 1-0 after Tuesday's first leg.
Lionel Messi. Photo: AFP
Bayern by contrast can all but look towards the semi-finals - where they are likely to play Real Madrid as the nine-time champions beat APOEL Nicosia 3-0 away on Tuesday -- after goals by Mario Gomez, his 11th of the campaign, and Arjen Robben edged them ever closer to the final which is being hosted at their stadium.
The results on Wednesday created a bit of history as it is the first time since it turned into the Champions League that none of the home sides in the quarter-final first legs have managed to score.
Chances were at a premium in Milan as the grizzled veterans such as Clarence Seedorf and Alessandro Nesta once again showed that the legs may get older but that class never goes away in denying Lionel Messi and his fellow stars from scoring.
Indeed Milan spurned the clearest chance as Brazilian star Robinho skied the ball over the bar from a few yards out in the opening minutes.
Barca appealed for a first-half penalty when Milan 'keeper Christian Abbiati clearly made contact with Chilean forward Alexis Sanchez - though the attacker had no chance of recuperating the ball - but Swedish referee Jonas Eriksson turned them down.
Milan coach Massimiliano Allegri said he was upbeat about his side's chances of reaching the last four.
"In the next match we can get two results from three (a win and a draw) so in respect to (before) tonight we have a slightly bigger chance (of progressing), notwithstanding the fact that Barca are the best team in the world," he said.
Barca coach Pep Guardiola said Milan's delight at the result spoke volumes about how they regarded his side.
"I admire their faith and self belief but it was always like this with the Milan of (Arrigo) Sacchi and (Fabio) Capello so they're happy with this 0-0," he said.
"They know that if they score, we need to score two and if they score two then we need three.
"But we're used to playing to win, we know it will be difficult."
Bayern Munich's win condemned Marseille to an eighth defeat in nine matches.
With Steve Mandanda suspended, Marseille coach Didier Deschamps chose to field third-choice goalkeeper Elinton Andrade but the move backfired in the 44th minute when the Brazilian allowed Gomez's shot to slip beneath him.
The 32-year-old was making his first appearance since January 2011 and he was beaten again by Robben in the 69th minute as Bayern took a commanding grip on the tie ahead of next Tuesday's return leg.
"We realised our objective by winning here without conceding any goals," said Bayern coach Jupp Heynckes.
"Marseille play emotional football, so it was very important for us to get this result tonight."
Heynckes, though, was less happy with the fact that German international midfield powerhouse Bastian Schweinsteiger picked up a booking that sees him suspended for the second leg.
"I am not happy that there were five yellow cards, especially that of Schweinsteiger's which was totally pointless and I told him as much."
It was a sixth consecutive success for Bayern, and defeat will have done nothing to sweeten the sour mood of the Marseille fans.
Having seen their team beaten seven times in succession prior to Saturday's 1-1 draw at Nice, OM's fans unfurled several protest banners ahead of kick-off, including one that read: "Deschamps and your players, get lost!