Anderlecht sprung to life midway through the second half when Guillaume Gillet's opening goal was quickly followed by a red card for Sturm's Thomas Burgstaller.
Matias Suarez then grabbed his fifth goal of the competition to keep the twice European Cup Winners' Cup holders and once UEFA Cup winners top of Group L with nine points from three games.
Group C leaders PSV Eindhoven, who won 1-0 at Hapoel Tel Aviv, and Group D leaders Sporting, who beat Vaslui 2-0, are the only other sides with maximum points after three games.
Mehdi Benatia gave Udinese an 89th-minute lead against Atletico despite mis-hitting his close-range shot and Floro Flores fired in from Emmanuel Badu's pass in the fourth minute of added-time to take the Italian side top of Group I.
As in Serie A, Udinese are unbeaten in the group.
Former European champions Steaua Bucharest had two players sent off as they lost 5-0 at Maccabi Haifa in Group J with leaders Schalke 04 winning by the same score at AEK Larnaca.
Group G leaders Metalist Kharkiv won 4-1 at Malmo despite playing more than half the game with 10 men. Argentine Jonathan Cristaldo was hero and villain for the Ukrainians as he scored their first goal but was sent off five minutes later.
Fernando Llorente converted two penalties in six minutes to give Athletic Bilbao a 2-2 home draw with Salzburg after the Group F leaders had trailed 2-0.
Twice UEFA Cup winners Tottenham Hotspur beat visitors Rubin Kazan 1-0 thanks to a sizzling free-kick from their Russia striker Roman Pavlyuchenko to take control of Group A.
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