Brazilian forward Luiz Adriano put Spartak 2-0 up against their European-chasing rivals in the 30th minute after some high quality build-up play.
The attack began in Spartak's half as Adriano picked up possession from behind the halfway line. The 30-year-old burst forward and passed the ball to Alexander Samedov, who sent it to Ze Luis.
Luis then cleverly backheeled it into the path of Adriano, who curled the ball into the bottom corner from the edge of the box.
Spartak went down to 10 men in the 85th minute but won the fiery contest 3-1 inside the Otkrytiye Arena. Victory has moved them within two points of second-placed Zenit and eight off city rivals Lokomotiv Moscow.
Spartak travel to Anfield to face Liverpool in the Champions League next week.
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