Fenerbahce started the game well and looked dangerous early on, with Moussa Sow firing a shot wide from 20 yards out in the sixth minute.
Sow looked the biggest threat throughout the first period and the forward went close again with a low effort that struck the post as Lazio struggled to find their comfort zone in Turkey.
Lazio's hopes of a positive result were dealt a big blow when Ogenyi Onzai was shown a second yellow card just after the break for a cynical foul on Cristian Baroni.
Fenerbahce almost immediately capitalised on their numerical advantage, with Raul Meireles striking the post from outside the box.
However, the hosts finally made the breakthrough with eight minutes remaining as Webo slotted the ball home from the penalty spot after Stefan Radu was punished for handling inside the area.
Dirk Kuyt completed the victory in the final minute of the match with a smart finish to give the Turkish side control of the tie.