It took only eight minutes for the deadlock to be broken with Middlesbrough taking full advantage of Jamie Carragher's suspension and a disorganised defence.
An inswinging Stewart Downing free-kick, after handball by Ryan Babel, found an unmarked Tuncay in the six-yard box and the Turkey star nodded home the simplest of finishes.
The visitors could have doubled their lead on 17 minutes as a throughball to Jeremie Aliadiere in the box looked inch-perfect only for Alvaro Arbeloa to shoulder the centre-forward off the ball just before he pulled the trigger.
Instantly the home side countered and a surging run and cross by Babel found Dirk Kuyt looking for his third goal in three games but the Dutch forward could only blast over from seven yards.
The Reds started to get a grip on the game and two goals in two minutes from Kop hero Torres looked to have finished off the Teessiders.
A weak back-header from Julio Arca on 28 minutes gave Torres the ball at his feet on the edge of the box and, with neat footwork, he took the ball around Mark Schwarzer before slotting into an empty net.
Liverpool took the lead almost straight from the re-start as they capitalised on a still dazed Boro defence.
A one-two between Fabio Aurelio and Babel created space for the former to cross for Torres who rifled his shot home.
Middlesbrough had the ball in the back of the net twice more before the break but an offside flag and a handball decision kept the home side one up at the break.
The second half saw the visitors come out of the blocks desperate to get back into the game but man-of-the-match Torres made it 3-1 on the hour mark as he netted his 21st goal of the season.
The Spanish wonder-kid looked second best to reach a long upfield punt until a mix-up outside the box between David Wheater and an on-rushing Schwarzer left the striker with the simple task of stroking the ball into an open goal.
Boro gave themselves a lifeline with seven minutes left when Arca found Downing on the left and, after skipping easily past Yossi Benayoun, the England international slotted a shot through a stranded Jose Reina's legs to make it 3-2.
However, Boro's chances evaporated when they were reduced to ten men when Aliadiere raised his hand to Javier Mascherano.