The result also means Everton have clinched fourth place to qualify for the Champions League for the first time.
Goals from Robert Pires, Jose Antonio Reyes and Francesc Fabregas put Arsenal six points ahead of Manchester United with two games left and their superior goal difference means they look certain to qualify directly for the Champions League.
Defeat ended Liverpool's hopes of finishing fourth and winning a place in Europe's premier club competition for next season with their city rivals Everton now certain of playing in the Champions League third qualifying round.
Champions Chelsea have 91 points followed by Arsenal on 80, Manchester United with 74 and Everton on 61. Liverpool are fifth level on 55 points with Bolton Wanderers and will have to be satisfied with a place in next season's UEFA Cup.
"(Everton) have had a good season and we've not played well away -- that's the difference," said Liverpool manager Rafa Benitez. "But to be in two finals in the same season is not easy and we have to improve next season in the Premier League".
Liverpool face AC Milan in the Champions League final on May 25 and also lost the League Cup final to Chelsea in February.
Even if Liverpool beat Milan they will not qualify for next season's competition after the FA ruled this week that only the top four in the Premier League can enter the Champions League.
But Liverpool will, in any case, need to perform much better in Istanbul to beat the Italians than they did in the first half against deposed Premier League champions Arsenal.
They started brightly enough but as soon as Pires curled in a delightful 20-metre free kick Liverpool started to look jaded after their dramatic Champions league semi-final victory over newly-crownedPremier League champions Chelsea on Tuesday.
Goalkeeper Jerzy Dudek had already denied Arsenal by tipping Lauren's bouncing far-post header on to the bar but the Pole was powerless to stop Pires's perfectly struck shot from flying into the top corner of the net after 25minutes.
Arsenal doubled the lead four minutes later through Spanish forward Reyes, who surged through a static defence and struck a firm left-footshot into the far corner.
Liverpool improved after halftime with the introduction of striker Djibril Cisse and winger Harry Kewell and their captain Steven Gerrard pulled a goal back with a deflected free kick from just outside the penalty area after 51minutes.
Gerrard then forced Jens Lehmann into a diving save with a fierce 25-metredrive and Arsenal, struggling to cope with the pace of Cisse and Kewell's trickery down the left, failed to reproduce their fluent passing of the first half.
Arsenal also missed the influence of their injured leading scorer Thierry Henry and endured anxious moments before Fabregas scored from close range in the dying seconds to confirm revenge for his team's 2-1defeat at Anfield earlier in the season.
"We're in a very strong position now, of course, and there's a good goal difference," Arsenal manager Arsene Wenger told Sky Sports referring to the battle with United for the runners-upspot. Arsenal's goal difference is 45 and United's is 33.
"We'lljust try to win our last two games and finish well. We'd prefer to be first but it was a good fight. We have rebuilt the team with a consistent run now and it's a good basis to improve from game to game and go into next season."