Chelsea secured a top three Premier League finish and entry into next season's Champions League group stages with a comprehensive win at Arsenal.
Alex powerfully headed Chelsea in front and Nicolas Anelka thundered in a 25-yard strike to dobule Chelsea's lead.
Arsenal's Kolo Toure put Ashley Cole's cross into his own net before a Nicklas Bendtner header pulled it back to 3-1.
The Gunners rallied but Chelsea wrapped up the win when Florent Malouda slotted in after Anelka's shot hit the post.
Arsenal will now be left to negotiate an open draw qualification for next season's Champions League, which could potentially pit them against a team from the German, Spanish or Italian leagues.
Both teams were coming off the back of elimination from this season's competition in midweek and, while the win will provide some consolation for Chelsea, Arsenal's misery will only be compounded by the loss.
It was a defeat that seemed unlikely when Arsenal burst out of the blocks and seemed set to score as they swarmed all over Chelsea.
Theo Walcott played a one-two with Robin van Persie, who appeared in an offside position, only to blaze high with his shot.
Walcott forced a save from keeper Petr Cech with a strike from a tight angle as Chelsea struggled to contain a home side showing the kind of determination and stylish passing that deserted them in their Champions League semi-final against Manchester United.
Abou Diaby sidefooted wide from a Walcott cross but might have been better leaving it for Cesc Fabregas, who was running in directly behind him and was better placed to shoot, as Arsenal again went close.
Chelsea appeared to be suffering from their last-minute Champions League exit to Barcelona, but did finally threaten through Malouda, though his weak effort was easily saved.
What are your thoughts on the game? Alexander Song turned and shot wide as Arsenal squandered another chance before they were punished by the visitors.
Drogba flighted in a free-kick for Alex to beat keeper Lukas Fabianski with a 12 yard header, which went in off the crossbar.
Former Gunners striker Anelka was allowed to run on the Arsenal goal from midfield and he took advantage by beating Fabianski from 25-yards to add a Chelsea second.
It was a harsh lesson in the benefits of clinical finishing for Arsenal and their predicament got worse after the break when a sliding Toure could only put the ball into his own net from Cole's cross.
A profligate Arsenal saw Walcott screw a shot across goal before substitute Bendtner's header from a Bacary Sagna cross inspired a late rally from Arsenal.
Cech saved well from Mikael Silvestre as Arsenal's pride saw them continue to battle away as they tried to protect a 21-match unbeaten league run.
But any faint hopes of a comeback were ended when Malouda struck late, although he appeared well offside as he passed home after Anelka's initial strike came back to him off the post.
Arsenal manager Arsene Wenger: "We have experienced a little bit of everything in football this week and only on the bad side.
"We created plenty of chances and should have been 2-0 up but we found ourselves 1-0 down.
"But the positive is going forward we did well, although defensively we certainly did not do as well."
Chelsea manager Guus Hiddink on his team winning after going out to Barcelona in the Champions League in midweek: "After the first 15 minutes the team reacted perfectly.
"I am very proud of them and they have shown they are one of the best in Europe tactically and mentally.
"I am very proud to work with these boys as they always react well."
Arsenal: Fabianski, Sagna, Toure, Silvestre, Gibbs, Walcott (Adebayor 68), Nasri, Song Billong (Denilson 67), Diaby (Bendtner 59), Fabregas, Van Persie. Subs Not Used: Mannone, Ramsey, Djourou, Eboue.
Goals: Bendtner 70.
Chelsea: Cech, Bosingwa (Ivanovic 77), Alex, Terry, Ashley Cole, Essien, Mikel, Lampard, Anelka, Drogba, Malouda (Ballack 88). Subs Not Used: Hilario, Di Santo, Kalou, Belletti, Mancienne.
Goals: Alex 28, Anelka 39, Toure 49 og, Malouda 86.
Ref: Phil Dowd (Staffordshire).
BBC Sport Player Rater man of the match: Chelsea's Nicolas Anelka (7.58 on 90 minutes).