Midway through the first half Sheriff came close to taking the lead against the run of play. Ricardinho played the ball through to Ismail Isa, who saw his low shot take a deflection of Younes Kaboul and crash against the post.
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At the start of the second half Christian Eriksen forced Tomic into a fine save from his long-range strike.
The home side finally made the breakthrough on the hour mark. Eriksen's chipped pass into the box deflected into the path of Erik Lamela, who calmy slotted the ball past the keeper.
Spurs were given the chance to double their lead a few minutes later when Lamela weaved his way into the box and was brought down by Djibril Paye. Jermain Defoe stepped up and fired his spot kick into the top corner to become the club's all-time top European goalscorer.
Lewis Holtby nearly scored the home side's third of the game in the final minute of the match but Tomic saved his effort.
The home side pushed for a late equaliser but Spurs dealt with their late surge and held out to book their place in the knockout stages.