The meeting, which took place at the Otkrytie Arena stadium in Moscow, ended with a score of 1: 0 in favor of the guests.
The only goal in stoppage time by the second half of the meeting was scored by Lirim Kastrati.
Spartak will play their next Europa League match on September 30 in Naples against Napoli.
The meeting starts at 19:45 Moscow time.
Earlier it was reported that Legia opened the scoring in the LE match with Spartak.