Ryan Babel handed Liverpool a slender advantage in their Europa League play-off - but Joe Cole's miserable week continued.
Debutant Christian Poulsen also had a goal disallowed as Liverpool carried a much greater threat after the break but the contest remains far from over with another 90 minutes to play.
Manager Roy Hodgson gave Steven Gerrard the night off and Liverpool 's dynamic captain was conspicuous by his absence throughout a drab opening 45 minutes.
Little of note occurred until Cole slipped in Babel on goal with a fine ball in stoppage time at the end of the first half and the Dutchman calmly clipped over the advancing Onur Kivrak.
Prior to that a Liverpool side retaining only four of the XI which opened the Barclays Premier League season against Arsenal lacked drive and direction.
Yet it was a rare moment of incision in the first period as both sides were restricted to long-range, and invariably off-target, free-kicks.
The more fluid attacks came from Trabzonspor and they gave Liverpool a scare when Reds right-back Martin Kelly was forced to head past his own post from a free-kick.
Selcuk Inan then flashed a header across goal from the resulting corner.
Yet neither goalkeeper had a save to make until Liverpool suddenly woke from their slumber with 45 minutes on the clock.
Cole found space and picked out the onrushing Babel with precision and the Holland international struck clinically.
Unfortunately for Babel , linked with a move to Wolfsburg this week, it proved to be his final touch of the game as he was replaced by Torres at the interval.
The Spaniard, feeling his way back into action after a groin injury, needed little time to show his class as he tested Kivrak with a long-range shot after a driving run.
Poulsen then won possession and combined well with Jovanovic before lashing another effort over.
Cole, sent off against Arsenal and anxious to get his Anfield career up and running, stepped up to take the spot-kick but shot tamely at Kivrak.
Liverpool were almost made to pay just before the hour as Umut Bulut showed great control on the edge of the area to turn and shoot but Reina deflected the ball over.
Torres, looking a different player from the one who laboured through the World Cup, rose to meet a Jovanovic cross but Kivrak grasped his firm header.
The Dane, however, had inched offside and the goal was ruled out.
Aurelio then found good space but dragged a shot wide from 12 yards.
For all Liverpool's dominance, the tie was still far from safe ahead of next week's return trip to Trabzon .
The visitors played out the closing minutes safely, perhaps hoping for another chance on home soil.