The Istanbul giants are now the favourites going into the second leg behind closed doors thanks to a pair of late strikes, but their cause was aided by Ogenyi Onazi's red card
A pair of late strikes from Pierre Webo - who netted a penalty - and Dirk Kuyt put the Turkish giants in the driving seat ahead of next week's return fixture which will be played behind closed doors at the Olimpico.
Despite playing on away soil, the visitors appeared to look most at home in the opening stages as they took the fiery atmosphere of the Sukru Saracoglu well within their stride.
Their midfield trio of Hernanes, Ederson and - most notably - Antonio Candreva did their best to drive Lazio forward and a succession of early warning shots rained in on Volkan Demirel.
But it was Fenerbahce who came closest to breaking the deadlock when Senad Lulic's poor clearance fell to Moussa Sow, but the Senegalese forward's effort was denied by the post.
The spark soon died out and a gritty battle ensued with both sides' defences firmly on top. Kuyt and Libor Kozak, two of the tournament's deadliest finishers, could barely feed off scraps.
However, the second half sprung into life with Ogenyi Onazi's red card for a second bookable offence. The Nigerian midfielder's lunge into the back of Cristian was excessive in the eyes of the referee.
The Biancocelesti were then fortunate to have rode their luck moments later as Raul Meireles, on the edge of the box, bent an effort towards goal which beat Federico Marchetti but deflected off the post.
And the ex-Cagliari goalkeeper was forced to stay on his toes as Meireles hit another attempt from distance before Sow and Webo began to infiltrate the Italians' box.
Nonetheless, Lazio were still in with a fighting chance after they showed great determination to continue plugging away in Istanbul, and Miroslav Klose's introduction further underlined their intent.
But, to the Romans' chagrin, it was not to be as Stefan Radu controlled Caner Erkin's header with his hand, allowing Webo to send Marchetti the wrong way from the penalty spot.
Their European fate then took a subsequent blow in the first minute of injury time as Erkin's vicious free kick stung the palms of the shot-stopper, leaving Kuyt to decisively sweep up the remains.