English teams may have suffered at the hands of Ronald Koeman in recent years, but the chances of the PSV and former Benfica coach claiming another scalp all but disappeared at the Philips Stadion as the Dutch league leaders were comprehensively outplayed.
Liverpool will welcome PSV to Anfield for the second leg of their quarter-final a week today with every confidence about progressing to the last four, where Chelsea or Valencia, who play their first leg this evening, will lie in wait.
Steven Gerrard surpassed Ian Rush as Liverpool's top scorer in the European Cup and its successor with his fifteenth goal in his 50th Champions League game, while Jamie Carragher made his 58th appearance in the competition, a club record.
The only sour note on another triumphant European night for Liverpool and Rafael BenÍtez, their manager, came when Fábio Aurélio was taken off on a stretcher with a ruptured Achilles. The Brazilian will undergo a scan today but he is almost certain to be ruled out for the rest of the season and possibly much longer.
Gerrard's header broke the deadlock in the 27th minute, John Arne Riise added a spectacular second goal and Peter Crouch completed the rout with his fourth in two games. "It was a bit embarrassing, to be honest," Gerrard said of breaking Rush's record. "He was someone I watched as a kid and I never dreamt I would be breaking any of his records. I don't think I will break any more. I am flattered but it is not important to me. Hopefully we can go all the way in the competition."
Koeman said that he "wouldn't belong on this planet" if he thought PSV, heavily depleted by injuries, could overcome a three-goal deficit at Anfield, but BenÍtez struck a cautious note. "You must be careful," the Liverpool manager said. "There is no room for complacency. We must approach the second leg seriously. It was a really good performance, but we are disappointed with the injury to Fábio. It seems serious.
"We broke some records and that is very positive for the club and the players. We want to see Stevie scoring goals and Carra breaking records.
"We are closer now [to the semi-final] but in football you need to play every game with people focused. This team is better than the one that won the Champions League [in 2005]. It's another year, another competition, but hopefully we'll go through."
Among those cheering on Liverpool was George Gillett Jr, their new co-owner. BenÍtez has been told that money will be no object in his attempts to build a team capable of winning the Barclays Premiership, although as Gillett witnessed, the Spaniard does not seem to have any trouble forging a winning side in Europe.
Liverpool's confidence for the second leg was reflected by the fact that Dirk Kuyt, their Holland forward, having already been cautioned twice in the competition this season, seemed to get himself booked in the second half.
Having escaped a caution for a foul, Kuyt appeared deliberately to obstruct a free kick and was shown a yellow card, which means he will sit out the second leg against PSV and not run the risk of missing the first leg of the semi-final. "That may be a positive," BenÍtez said.