The Dutchman sent Pep Guardiola's men ahead in the midweek clash before Thomas Muller doubled the lead shortly after the break at the Allianz Arena
Fresh from scoring twice in a 4-0 win at Augsburg on Saturday, the Netherlands international was on target again in a typically dominant performance in Bayern's last match at the Allianz Arena before the mid-season break.
Head coach Pep Guardiola labelled Robben's recent performances as "unbelievable" after the Augsburg win.
And he reached a century of Bayern goals with a close-range header in the 41st minute from a Franck Ribery knockdown, the Frenchman having himself reached 100 goals against Bayer Leverkusen this month
The leaders, who are unbeaten in the league this term, extended their lead three minutes after the break through Thomas Muller's seventh top-flight goal of the season, while Juan Bernat also rattled the post.
Bayern have now won 17 of their last 20 Bundesliga matches and, with second-placed Wolfsburg not playing until Wednesday, their lead at the top of the table extends to 12 points.
The hosts were uncharacteristically wasteful in the final third in the opening 20 minutes, but Bayern soon found their stride and Muller headed over when stretching to meet Ribery's cross from the left byline.
Muller was at the heart of Bayern's next chance in 22nd minute, the German turning Marc-Oliver Kempf sharply in the area before stabbing narrowly wide when off balance.
Robben then tried his luck with a half-volley from distance, before Roman Burki made a fine one-handed stop to deny Mario Gotze's eight-yard side-footed volley that would have found the bottom right-hand corner.
Bayern were dealt a blow when Mehdi Benatia limped off to be replaced by Jerome Boateng, but the home fans were celebrating Robben's landmark four minutes before the break.
Xabi Alonso's brilliant clipped pass was nodded back across goal by Ribery and Robben stooped low to head home.
Burki did well to keep the score at just one before half-time when he tipped Muller's close-range shot onto the post.
Robert Lewandowski took a knock to his right leg in the first half and was replaced by Bastian Schweinsteiger at the break.
The change did not affect Bayern's flow, though, and Muller made it 2-0 in the 48th minute.
Robben was again involved with a superb cross-field pass that picked out Bernat whose flicked shot looped onto the crossbar and Muller was on hand to head home the rebound.
Muller almost had a second when put his header from Ribery's cross narrowly past the post, before Burki made a smart stop from Dante's header.
Freiburg had Burki to thank again 20 minutes from time when the goalkeeper made a fine fingertip save from Bernat's strong effort, before the Spaniard was then denied by the frame of the post.
Admir Mehmedi then threatened with a rare shot for the visitors, but his effort from 20 yards hit the side-netting.
Robben and Bernat were both brilliant denied by Burki again as Guardiola's men eyed more goals in the closing stages, but it stayed 2-0 as Bayern made it 12 home Bundesliga wins in a row against Freiburg.