Benfica defender Luisao scored a late goal to give his team a slender lead in their Champions League tie.
Luisao's goal has given Benfica a lead to take to Anfield
Both sides had struggled to create chances on a bumpy pitch and before the goal Jose Reina was hardly tested.
Reina had showed quick reactions to get to the ball before Simao Sabrosa did and later the Liverpool keeper saved well from midfielder Armando Petit.
It was Petit whose free kick set up the Benfica goal, Luisao powering a header past the flat-flooted Liverpool keeper.
Liverpool had plenty of possession, but laboured to find strikers Fernando Morientes and Robbie Fowler.
Manager Rafael Benitez had opted to leave Steven Gerrard on the bench for Liverpool with the midfielder suffering from a slight knee injury.
Just past the half-hour mark Liverpool's midfield needed a further rejig after Mohamed Sissoko was stretchered off after being kicked in the head by Beto.
The Brazilian Beto, who himself had been on the end of a nasty challenge from Luis Garcia in the first minute, was booked for his challenge, while Sissoko was replaced by Dietmar Hamann.
Struggling in the Portuguese league in recent weeks, Benfica took a while to threaten the Liverpool defence.
But on 25 minutes Laurent Robert threaded a pass through to Simao, whose darting run was well anticipated by Reina, who got to the ball first.
In that cagey opening Robert proved Benfica's most dangerous forward, swinging a couple of testing corners in and then going on a run, before he was fouled by John Arne Riise.
Fowler was involved in a couple of Liverpool half-chances in a less than enthralling first half.
The Liverpool striker first unsettled Marcelo Moretto with an aerial challenge that resulted in the Benfica goalkeeper dropping the ball.
Fowler also caused concern in the Benfica penalty area with a flick following a Xabi Alonso free-kick.
Early in the second half Luis Garcia sliced a volley wide after Luisao failed to get sufficient distance with a header.
Just past the hour Petit almost surprised Reina with a long range shot, an effort that forced the Liverpool goalkeeper to quickly retreat.
With the game still goalless after 76 minutes Benitez introduced Gerrard in place of Morientes as Liverpool sought to provide their defence with further protection.
But with time running out for Benfica, Petit came to his side's rescue, picking out Luisao, whose header flew past Reina into the corner of the goal.
Benfica: Moretto, Alcides, Luisao, Anderson, Leo (Ricardo Rocha 87), Robert (Nelson 76), Petit, Beto (Karagounis 58), Manuel, Simao, Nuno Gomes.
Subs Not Used: Quim, Mantorras, Karyaka, Marcel.
Goals: Luisao 84.
Liverpool: Reina, Finnan, Carragher, Hyypia, Riise, Luis Garcia, Sissoko (Hamann 35), Alonso, Kewell, Morientes (Gerrard 78), Fowler (Cisse 65).
Subs Not Used: Dudek, Crouch, Traore, Warnock.
Booked: Luis Garcia, Hamann.
Ref: Konrad Plautz (Austria).