Keane celebrates with Torres after scoring his first Liverpool goal
Robbie Keane's first goal since his £20.3m move from Tottenham helped Liverpool ease to victory over PSV Eindhoven in Champions League Group D.
Dirk Kuyt put the Reds ahead after four minutes, following up after Andreas Isaksson saved Fernando Torres' volley.
Keane made it 2-0 before half-time when he hooked home Torres' bouncing cross.
Steven Gerrard wrapped up the win with a ferocious free-kick - his 100th goal for Liverpool - before Danny Koevermans bundled home a consolation for PSV.
There are sure to be sterner tests ahead for Liverpool in Europe this season than the visit of the Dutch champions but Reds boss Rafa Benitez has plenty of reasons to be satisfied after his side's convincing display.
PSV clearly came to Anfield with the intention of frustrating their hosts but their hopes of implementing that plan only lasted untol Kuyt broke the deadlock.
Visiting keeper Isaksson did well to deny Torres, who had ghosted in unmarked to meet Steven Gerrard's cross, but he should have done better with Kuyt's shot which span out of his grasp and into the top corner.
From then on it was hard to see how Huub Stevens' side were going to emulate Stoke City, the only side to deny the Reds victory at Anfield this season.
PSV persevered with five men across the back - which at least kept Liverpool quiet immediately after they had scored - but with Nordin Amrabat on his own up front they were restricted to long-range efforts in their search for an equaliser.
Liverpool, meanwhile, continued to look menacing and, even before his goal, Keane might have had a penalty when he was tripped in the area by Carlos Salcido.
Torres was next to threaten, rising unmarked to head a Fabio Aurelio corner wide, and it was fitting that he was involved in Liverpool's second goal on 34 minutes.
Much has been made of the potential potency of Torres' partnership with Keane but the common consensus is that it will be the Republic of Ireland international who will be creating chances for his Spanish team-mate.
The opposite was the case here, with Torres combining well with Kuyt on the right before sending over an inviting cross that Keane despatched past the helpless Isaksson to end his Liverpool goal-drought in his 11th game for the Reds.
Aside from his fruitless spell with Inter Milan, Keane has never had to wait this long for his first goal for a club and the relief in his trademark tumbling celebration was obvious.
Steven Gerrard lets fly with the free-kick for his 100th Liverpool goal
PSV, to their credit, continued to work hard and Otman Bakkal and Amrabat both sent shots skidding wide of Pepe Reina's goal.
But Liverpool were still more than comfortable and Torres should have made it 3-0 when he ran on to Jan Kromkamp's sloppy backpass only to see his attempted flick drift wide.
The third goal did arrive on 74 minutes, courtesy of Gerrard, who marked his century of Reds goals with an absolute scorcher.
Gerrard, so often Liverpool's saviour in the past, has scored many more crucial goals for his club but few have been better strikes than his free-kick, which left Isaksson with no chance.
That should have capped a fine night for the Anfield faithful but instead it was PSV who had the final word, Koevermans meeting a deep cross and getting enough on the ball to beat Reina.
The end result was never in doubt, however, and Liverpool will head into back-to-back fixtures with Atletico Madrid in a strong position to qualify for the knock-out stages.
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