By Chris Bevan
Craig Bellamy celebrated his goal by imitating a golf swing
Deco nodded Barca in front from Gianluca Zambrotta's precise cross.
But Liverpool dug in and they levelled when Barca keeper Victor Valdes let Bellamy's header creep over the line.
Barca poured men forward but the Reds took the lead when Bellamy teed up Riise to fire home and they held on to win despite seeing Deco hit the post.
The pre-match headlines had been all about an alleged training camp fracas between Bellamy and Riise - but both were in Liverpool's starting line-up and did not take long to link up as the Reds made a confident start to the game.
Inside the first four minutes Steven Gerrard released Riise and his driven cross from the left was only just too strong for the Welshman.
But an attacking Barca line-up - with Javier Saviola flanked up front by Ronaldinho and Lionel Messi - did not take long to get into their stride.
Saviola had already been harshly called offside after breaking clear when Deco had a dangerous shot blocked by Jamie Carragher.
So it was no real surprise when the home side took the lead on 14 minutes.
Zambrotta escaped Gerrard on the left and, with Risse napping, his cross found Deco on his own at the far post to score with a bullet header.
It almost got worse for Rafa Benitez's side as Barcelona looked to press home their advantage.
The Reds had no answer to the home side's quick incisive passing that gave them two more chances in quick succession.
First Saviola shot wide after getting past Carragher, then Jose Reina had to make a good low save to deny Deco after he had ghosted on to Messi's through ball.
But Liverpool rode the storm and two minutes before half-time they were handed an unlikely route back into the game.
Much has been made of Barca's recent defensive vulnerability and it reared its head again here, thanks to a disastrous mistake by goalkeeper Victor Valdes.
John Arne Riise celebrates Liverpool's winner
Bellamy had already escaped the Barcelona defence once to nod Gerrard's free-kick against the side-netting and he was soon at it again.
The Wales striker was all on his own to meet Xabi Alonso's cross and, although Valdes caught the ball, he carried it over the line before pushing it back out.
Dirk Kuyt followed up to make absolutely sure of the equaliser but it was not a surprise to see Bellamy claim the goal after his turbulent week - and he celebrated it with a golf swing.
Frank Rijkaard's side seemed to run out of ideas and, in the absence of any clear gameplan, settled for sending more men forward.
That played into Liverpool's hands and another Valdes error gave them their first chance of the second half when he picked up a back-pass with 20 minutes left.
The keeper saved Alonso's shot with his feet and was glad to see Kuyt head over when the midfielder swiftly sent over an inviting cross.
But Benitez did not have to wait long to see his side go ahead.
Reina saved well from Saviola and, when Liverpool came forward again, Valdes denied Kuyt - but the ball fell for Bellamy who fed Riiise to sweep the ball home.
There was still time for Deco to send a free-kick curling against the post with Reina beaten but Liverpool held on for a famous victory.
Barcelona: Valdes, Belletti, Marquez, Puyol, Zambrotta, Xavi (Giuly 65), Motta (Iniesta 54), Deco, Messi, Saviola (Gudjohnsen 82), Ronaldinho.
Subs Not Used: Jorquera, Van Bronckhorst, Thuram, Oleguer.
Booked: Belletti, Zambrotta.
Goals: Deco 14.
Liverpool: Reina, Arbeloa, Carragher, Agger, Riise, Finnan, Sissoko (Zenden 84), Alonso, Gerrard, Bellamy (Pennant 80),Kuyt (Crouch 90).
Subs Not Used: Dudek, Hyypia, Gonzalez, Mascherano.
Booked: Agger, Kuyt, Sissoko, Bellamy.
Goals: Bellamy 43, Riise 74.
Att: 88,000
Ref: Kyros Vassaras (Greece).
The first leg of the round of sixteen in the  was completed on Wednesday, with at least one controversial result, and a bag full of ties.  The leg began on Tuesday with four games, and the other four were played the next day, including reigning champions FC Barcelona of Spain.

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