Daniel Agger gave his side the perfect start in the ninth minute but things took a turn for the worse when Ryan Babel was dismissed on the half-hour for thrusting a hand in Luisao's face.
Oscar Cardozo wasted numerous chances before converting two spot-kicks but with an away goal Rafael Benitez's side still have hope for the return leg.
Benitez had said before the game he did not expect the Portuguese league leaders to target striker Fernando Torres - but he was wrong.
The Spain international was on the receiving end of some hefty challenges which Swedish referee Jonas Eriksson seemed content to leave unpunished.
It was no surprise to see Torres withdrawn before the end, firstly to avoid injury and secondly to prevent him getting a booking which would rule him out of the second leg at Anfield.
Playing against a backdrop of a cacophony of noise and, in the second half, a stream of fireworks aimed at Jose Reina's goal, Liverpool had the ideal start.
Maxi Pereira's ninth-minute foul on Steven Gerrard gave the Liverpool captain a chance to whip in a dangerous free-kick from just left of the penalty area.
However, with the hosts massed around the six-yard area the midfielder fooled everyone by rolling a low pass in towards the penalty spot where Agger produced a classy backheel into the corner of the net.
It was reminiscent of a similar move which saw the Denmark defender score in the Champions League semi-final against Chelsea in May 2007, although that one was hit with more power.
Fortunately for Liverpool, Benfica's European top scorer this season, Cardozo, could not show the same composure as he squandered three good chances in quick succession.
The profligacy was contagious as Pablo Aimar's usually reliable first touch let him down as he looked to beat Reina, making his 250th appearance for the club.
Ramires was next to head over at the far post from a cross by Di Maria, whose shot from 25 yards fizzed just over Reina's crossbar in the 28th minute as the pressure built.
The highly-charged atmosphere exploded on the half-hour when referee Eriksson appeared to completely lose control.
Centre-back Luisao took exception to a tackle by Babel and subsequently hacked right through the back of Torres, who had already been on the end of some severe punishment.
A melee ensued in which Luisao continued his protest at Babel and the Dutchman responded by pushing the Brazilian in the face.
The Swedish official showed the Benfica defender a yellow card and then flashed a red at Liverpool's Holland international - sparking a sustained but fruitless protest by Liverpool's entire team.
David Luiz was next to go into the book for clattering Torres in the 37th minute and the Spain striker thought he had exacted the perfect revenge when he volleyed home Julio Cesar's weak punch from Gerrard's free-kick - only to be denied by an offside flag.
Emiliano Insua was booked for pulling back Di Maria just before the break, ruling him out of the second leg.
Within four minutes of the restart Cardozo planted one header straight at Reina and the other over from five yards and you sensed just maybe it was going to be Liverpool's night.
But, after a stray firework landed close to the fourth official next to Reina's goal, their luck changed.
Cardozo's 59th-minute free-kick rattled back off the right-hand post and when Aimar went down under Insua's tackle chasing the rebound Eriksson pointed to the penalty spot.
This time Cardozo finally hit the target to beat Reina.
In the 76th minute Torres had a glorious chance to put his side back in front - and score his first Liverpool goal on foreign soil since March 11 2008 - but with only Cesar to beat he dragged his shot wide from Kuyt's pass.
It was to prove costly as two minutes later Di Maria's cross hit Carragher as he slid in to tackle and the fourth official signalled a penalty for handball.
The defender was booked and Cardozo scored his second spot-kick of the night.
With more fireworks raining down behind Liverpool's goal towards the end Benitez's side were fortunate to leave Lisbon with just a one-goal deficit.