Gomez gave Bayern the lead just before half-time when Robben's defence-splitting pass sent him clear and his shot beat Elinton Andrade who should have done better.
The Bundesliga side, who are desperate to reach the final that will be staged in their own stadium, dominated the second half and the outstanding Robben doubled their lead after 69 minutes to put them firmly in the driving seat for next Tuesday's second leg.
Marseille had a few early chances, notably when Rod Fanni's header was parried by Manuel Neuer into the path of Loic Remy only for the France striker to lash his close-range shot wide.
The French club's task will be even harder in the second leg as holding midfielder Alou Diarra picked up a yellow card and will be suspended.
"We did some good things until the opener but their goal really hammered us considering what we had achieved before they scored," Marseille manager Didier Deschamps told reporters.
"The second half was much harder. We faced a very good team. We played with heart but there's a gap between the two teams and everybody saw that."
Bayern's coach Jupp Heynckes had said on the eve of the game that Marseille's main strength was their passion and the Stade Velodrome atmosphere but the disenchanted home fans were silent throughout apart from when they were booing former winger Franck Ribery on his first return to his old club.
All the noise came from Bayern's fans who had plenty to cheer about after a slightly nervy start.
There was nothing wrong with Gomez's finish but the Bayern counter-attack began when Philipp Lahm handled the ball as he claimed it from Mathieu Valbuena.
Robben produced a moment of real class to double the lead, playing a neat one-two with Thomas Muller before sliding a shot beyind Marseille's third-choice keeper Andrade.
"We achieved our goal which was winning here while keeping our goal clean," Heynckes told reporters. "I'm glad with the way we played the match.
