The Algeria international notched the matchwinning goal to give the Yellow Canaries a first leg advantage at Sukru Saracoglu Stadi
On the back of their loss to Kayserispor on Friday, the Yellow Canaries bounced back to winning ways with the Algeria international playing a key role.
The 30-year-old who last scored a goal on December 6 against Giresunspor ended the drought in the 21st minute of the encounter.
The Leicester City loanee fired home from close range after pouncing on a loose ball in the box to give his side a first-leg advantage at the Sukru Saracoglu
The visitors had a chance to level from the penalty spot through Robert Mak but goalkeeper Harun Tekin saved the kick.
Slimani featured for the entire duration of the game while Nigerian winger Victor Moses was replaced with five minutes left to play.
Ghana international Andre Ayew was introduced in the 72 minutes of the encounter for Eljif Elmas.
This season, Slimani has scored three goals in the tournament and five in all competitions.
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The second leg will take place on February 21 at Saint-Petersburg Stadium.