Liverpool stumbled to an 11th defeat away from home allowing rivals Everton to qualify for the Champions League.
Arsenal's win means they are almost certain of finishing in second place.
Robert Pires' precision free-kick put Arsenal ahead and soon after Jose Antonio Reyes' run and angled shot exposed some lax Liverpool defending.
Steven Gerrard's deflected free-kick on 51 minutes gave Liverpool hope but in stoppage time Cesc Fabregas rounded off a sweeping move for Arsenal's third.
As so often this season, Liverpool packed their midfield, leaving Milan Baros up on his own in attack in an attempt to stifle Arsenal.
For the start of the second half manager Rafael Benitez introduced Djibril Cisse and Harry Kewell, a change that saw a more ambitious approach, but the poverty of their play in the opening period gave them too much of a mountain to climb.
A flavour of Liverpool's insipid first-half display came on 10 minutes when a mistake from Sami Hyypia and a Jerzy Dudek fumble allowed Reyes to score from close range, only for the goal to be disallowed for offside.
Dudek did better to thwart Lauren, pushing the Cameroonian's header on to the bar, though the Arsenal defender fluffed his shot in trying to convert the rebound.
Arsenal had their own lucky escape when John Arne Riise eluded the Arsenal defence to collect Dietmar Hamann's pass.
With Luis Garcia calling for the ball, Riise opted to shoot, an effort deflected away by Jens Lehmann's feet.
By the midway point of the first half Arsenal had gathered a head of steam, demonstrating wonderful individual play allied to a great collective ethic.
First Pires curled a shot narrowly wide and soon after the Frenchman punished Liverpool following Hamann's crude tackle on Patrick Vieira.
From just outside the box Pires flighted the ball over the Liverpool wall and into the net, with Dudek only able to look on from the other side of the goal.
Reyes waltzed his way through the Liverpool defence and slipped the ball past the advancing Dudek for the second.
After the interval Liverpool quickly pulled a goal back, Fabregas turning his back on Gerrard's free-kick and deflecting the England international's shot past Lehmann.
Just past the hour a superb Gerrard pass bisected the Arsenal defence but Cole sprinted across to get in a block tackle on Luis Garcia.
Gerrard then unleashed a fierce drive that produced an athletic Lehmann save.
Liverpool kept plugging away but with time running out substitute Dennis Bergkamp flicked the ball through to Fabregas, who rattled a shot past Dudek.
Arsenal boss Arsene Wenger:
"The injuries are serious. Gilberto has a recurrence of ankle injury, Patrick Vieira has hurt his knee, while Robert Pires turned his ankle.
"It's a little bit worrying and we will have to see how they are on Monday.
"What's positive with so many young players is the quality of the game we can reach - it makes me optimistic."
Liverpool boss Rafael Benitez:
"We played well for the first 15 minutes, but when we conceded a goal we put our heads down and we didn't play well for the rest of the first half.
"We played with a higher tempo in the second half, but now we have to prepare for the European Cup final.
"I am disappointed by the things we have done away from home.
"To be in two finals is not easy, but we haven't done well in the Premiership."
Arsenal: Lehmann, Lauren, Toure, Senderos, Cole, Fabregas, Vieira, Silva, Pires (Edu 68), Van Persie (Bergkamp 68), Reyes (Aliadiere 86). Subs Not Used: Campbell, Almunia.
Goals: Pires 25, Reyes 29, Fabregas 90.
Liverpool: Dudek, Finnan, Carragher, Hyypia, Traore, Hamann (Smicer 68), Luis Garcia, Gerrard, Alonso, Riise (Kewell 45), Baros (Cisse 45). Subs Not Used: Carson, Biscan.
Booked: Baros, Hamann.
Goals: Gerrard 51.
Ref: G Poll (Hertfordshire).