Hartson was a constant menace to the Liverpool defence Photos from Anfield

Celtic sent Liverpool crashing out of the Uefa Cup with a convincing victory at Anfield.

An Alan Thompson free-kick and a stunning strike from John Hartson secured a relatively comfortable passage for Martin O'Neill's side into the semi-finals.

It was another lacklustre display from a Liverpool side who are left with little to play for in a disappointing season.

After a 1-1 draw in Scotland, Celtic knew they needed to come out and attack from the off and they were more than willing to do so.

Liverpool's Dietmar Hamann went close in the early stages with a vicious shot after Vladimir Smicer had dummied a Danny Murphy corner.

But Celtic were soon on the offensive with Thompson intercepting a stray Hamann pass in a dangerous area before shooting over.

Henrik Larsson curled a free-kick from 30 yards that Jerzy Dudek acrobatically turned around the post.

Larsson's strike partner Hartson was a constant menace for the Liverpool defence and he was just off target with two headers.

KEY MOMENTS 23 mins: Heskey blazes wide after being set up by Owen 45 mins: Thompson scores from a free-kick on the stroke of half-time 81 mins: Hartson secures the win with a stunning strike

He nodded just over from a Paul Lambert free-kick before heading wide from a fine driven cross by Larsson.

The home side had their chances, with Emile Heskey slicing well wide from close range after a brilliant run from Michael Owen.

Steven Gerrard went even closer with a fine strike from well outside the area that Rab Douglas did well to parry out for a corner.

But for much of the opening period Liverpool looked content to sit back and absorb the pressure, knowing a 0-0 draw would be good enough.

But that was always likely to be a dangerous game against side who went into the tie having scored in their previous 49 outings.

It was little surprise when they made it 50 on the stroke of half-time when Thompson scored from a free-kick.

I missed an important penalty on Sunday so hopefully that goal tonight made up for that a bit. John Hartson

It was a decent effort from the former Bolton winger, but there will be questions asked of the Liverpool wall for allowing the shot to slide underneath them and past a stranded Dudek.

Larsson could have added a second when he was one-on-one with the keeper, but Jamie Carragher got back well to deflect his first effort and the Swede's second attempt was wide of the mark.

Gerrard was superbly put through by Owen but with just Douglas to beat the midfielder fired straight at the keeper.

Dudek had to be at his best to tip over as Larsson again threatened from a corner.

But he could do little about Hartson's late strike that made sure of the win and a place in the semis at the expense of their English rivals.

Liverpool: Dudek, Carragher, Traore, Hyypia, Riise, Murphy, Hamann, Gerrard, Smicer (Baros 56), Heskey, Owen.
Subs Not Used: Arphexad, Berger, Diao, Biscan, Cheyrou, Mellor.

Celtic: Douglas, Mjallby, Balde, Valgaeren, Sylla (Smith 86), Lennon, Lambert (McNamara 73), Petrov, Thompson, Larsson, Hartson.
Subs Not Used: Marshall, Laursen, Maloney, Guppy, Crainey.

Booked: Mjallby, Sylla, Thompson, Douglas.

Attendance: 44,238

Referee: Markus Merk (Germany).