Alex set Chelsea on the way to victory with his header
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 double 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.
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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.
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