Schweinsteiger's 8th minute goal put Bayern in a comfortable position early on, but it was Robben who provided the insurance in the second half with his 72nd minute strike.
Bayern had a plethora of opportunities throughout the match to extend its lead, but missed chances, along with a heroic display from Zurich goalkeeper Johnny Leoni, helped keep the scoring to a minimum.
With the win, Bayern takes a two-goal advantage to Switzerland for the second leg on Aug. 23, with the aggregate winner advancing to the group stage.
Zurich, runners-up in last season's Swiss league, will need to win defeat Bayern by three goals, as it was unable to produce a crucial away goal.
Dinamo Zagreb 4, Malmo 1
Zagreb, Croatia - A Sammir brace helped Dinamo Zagreb dismantle Swedish club Malmo 4-1 to open the Champions League playoff-round series on Wednesday.
Sammir and Agon Mehmeti traded first half goals as Dinamo and Malmo were tied 1-1 at halftime. But the Croatian club impressed in the second half, as goals from Ante Rukavina, Sammir, and Fatos Beciraj handed Dinamo a dominating win.
The second leg is at Malmo on Aug. 23. The aggregate winner advances to group play.
Maccabi Haifa 2, Genk 1
Haifa, Israel - Maccabi Haifa opened its Champions League playoff-round series against Racing Genk with a 2-1 win in Israel on Wednesday.
First half goals from Weam Amasha and Vladimer Dvalishvili proved to be all the Israeli club would need to win the match, despite conceding a goal to Genk's Elyaniv Barda in the 61st minute.
The road goal gives the Belgian side a chance to overturn the result in the second leg, as Genk will host the return match on Aug. 23. The aggregate winner advances to group play.
Odense 1, Villarreal (Spain) 0
Odense, Denmark - Odense pulled off a shock win over Villarreal, as the Spanish club opened it Champions League playoff-round series with a 1-0 road loss on Wednesday.
The Danish club left it late, as Hans Henrik Andreasen recorded the game's only goal in the 84th minute to put Villarreal in a considerable hole for the second leg.
Villarreal will host the return match on Aug. 23 with the aggregate winner of the series advancing to the group stage.
Wisla Krakow 1, APOEL 0
Krakow, Poland - Polish club Wisla Krakow earned a 1-0 win over APOEL on Wednesday to claim an advantage in its Champions League playoff-round series.
Krakow's Patryk Malecki got the game's lone goal in the 71st minute. The second leg will be played at APOEL on Aug. 23 and the aggregate winner will advance to group play.