Within the first 10 minutes, both sides created movement in front of goal, and Fedor Smolov came close for Anzhi with a shot from 19 metres out, which drifted wide of the post.
Genk had the chance to respond when Sekou Cisse dodged past his opponent in the final third, but none of his teammates could latch on to his low pass into the area.
After Anzhi were awarded a free kick, Aleksandr Bucharov met the ball and unleashed a header towards the right post, but it was blocked before it could find the back of the net.
Bucharov wasted another chance a matter of minutes later when he tried a second header towards goal, but it soared narrowly wide of the right post.
Genk were able to gradually dominate possession in the early stages of the first half with some one-touch passing between Kalidou Koulibaly and Thomas Buffel, but they were unable to make the most of their build-up play.
Anzhi managed to create a goalscoring opportunity when Oleksandr Aliev stormed into the box to latch on to a low pass and hammer the ball towards goal, but his effort was blocked by the defender.
Just upon reaching the end of normal time, Anzhi were dealt a blow when Ilya Maksimov was given a straight red card for a dangerous tackle with a matter of minutes remaining in the match.
Despite some chances for both side during the clash, neither side could find the breakthrough by the final whistle.