Jamie Carragher's farewell Liverpool appearance before retirement ended with a comfortable win over relegated QPR.
The Reds were denied an early goal when Philippe Coutinho's header following a corner seemed to cross the line.
QPR then had a penalty appeal turned down for a Lucas Leiva trip on striker Loic Remy before Brazilian Coutinho netted with a 25-yard strike.
Carragher almost scored a dream goal on his departure only for his long-range shot to bounce back off the post.
The central defender was substituted to a huge ovation late on, with Anfield bursting into a rendition of 'we all dream of a team of Carraghers' on his exit.
Earlier, there had been a huge roar as the former England international walked out for his 737th club appearance. He was given a guard of honour by both sets of players, with the Kop paying its own tribute by displaying a mosaic of his initials and squad number.
The 35-year-old went on to bow out of the game with a clean sheet, while relegated QPR said their own goodbye to the Premier League with a defeat which left them bottom of the table.
As the clock ticked down on Carragher's time at Anfield, Jordon Ibe was handed his first-team debut by Brendan Rodgers and the 17-year-old winger impressed by setting up his side's goal in the 23rd minute.
After Coutinho's goal that never was and the rejection of Remy's penalty appeal, Ibe jinked in from the left and laid the ball off for playmaker Coutinho to send an unerring strike into the bottom corner.
Carragher escaped a booking from referee Martin Atkinson when he tried to punch in a Coutinho cross at the far post as the Reds threatened a second.
QPR rarely troubled the home side's goal but French forward Remy, who was recently arrested on suspicion of rape before being released on bail, sent a 20-yard shot narrowly wide.
Bobby Zamora also had a chance for the visitors only for the striker to fail to connect with an attempted side-footed effort after Martin Skrtel could not prevent a low cross from reaching him.
Liverpool, though, were the team with a firm grip on the match and QPR keeper Rob Green smartly kept out deflected strikes from Jose Enrique and Glen Johnson, while an angled Ibe shot went wide of his far post.
The Kop were willing Carragher to score and he almost did so in spectacular style only for his fierce 30-yard shot to hit the post.
Liverpool's victory would have been more emphatic had it not been for Green but the final word inevitably belonged to Carragher, who was loudly cheered when he was substituted shortly before the end.
Liverpool manager Brendan Rodgers:
"The win marks a terrific end to the season for us. We would love the season to continue as we have found our feet and form. [But] we've got work to do during the summer in terms of reinforcing the group.
"Carra is a true great. This is a guy, who after 737 games, is a true legend of this club. His performance was immaculate. I only wish for him and his family that his strike would have gone in. He gets credit for defensive qualities but he is also a great technical player.
"It has been a pleasure working with him. My only regret is that I would have liked to have had many more years and games working with him."
QPR boss Harry Redknapp:
"We've been close in a lot of games but lacked quality to turn those close games around.
"We didn't have the quality to stay in the Premier League. We need to improve that in the summer with lads who want to work hard and do well for QPR.
"We've got no divine right to come straight back up. We'll have to work hard. I've inherited a group with some good professionals and also with people who are not so good.
"That has been the problem. Lots of them can't get up early enough to get to training on time."