Chelsea dominated all but the last 20 minutes of the first half. They rode their luck, defended with typical efficiency and could have had three more goals in breakaways.
They ended Arsenal's record of 13 successive Premiership home wins and they have not conceded a league goal since November 6.
The Gunners are eighth, 20 points behind the leaders and five behind north London rivals Tottenham. At this rate, they will struggle to qualify for the Champions League.
This was the first time Arsenal have lost three successive Premiership games during Arsene Wenger's nine years in charge.
The speculation about Sir Alex Ferguson's future has deflected attention from Wenger's disappointments. The Gunners have fallen out of the top three for the first time in his reign.
They are clearly missing the influence of midfield powerhouse Patrick Vieira, sold to Juventus in the summer. Their squad lacks strength in depth. By contrast, the champions boast experienced options for every position.
Ashley Cole and Gael Clichy are still injured, so Arsenal reshuffled their defence with Kolo Toure starting at right-back and Lauren switching to the left.
Claude Makelele returned after missing five games with a ligament strain to anchor a five-man Chelsea midfield. Arsenal dropped Robin Van Persie deep to match the champions' five.
Chelsea pressed ruthlessly in the first 20 minutes. The Gunners could not win the ball, let alone keep it.
Joe Cole stubbed his shot from Didier Drogba's second-minute header after Frank Lampard intercepted Alexander Hleb's misplaced pass.
Jens Lehmann tipped over Lampard's inswinging free-kick, before Philippe Senderos' last-ditch tackle halted Drogba as he tried to round Lehmann.
Then Arsenal almost scored. Hleb fed Henry who hit a right-foot shot against the outside of a post. A minute later, Van Persie swept Ljungberg's pass into the Chelsea net, but the goal was disallowed for offside against Henry.
Arsenal were galvanised. They began to compete physically. They were furious when Michael Essien elbowed Lauren and was booked.
They felt even worse in the 39th minute when Robben beat the offside flag and lost Toure. He shot across Lehmann and the ball went in off the inside of an upright.
Robben broke clear again straight after half-time, to be felled by Senderos, but Lampard's free-kick bounced away off Drogba.
Henry tried to thread Hleb through, but Chelsea's massed ranks crowded him out, while Arsenal's intricate football foundered against the champions' suffocating defence.
The Gunners really do lack alternatives, such as a tall striker who can head the ball.
Robben wasted a great chance to kill the game, when he broke on to Ricardo Carvalho's clearance. He hesitated with his shot and Lauren cleared. Lehmann saved Robben's low shot after another incisive counter.
Arsenal sent on Dennis Bergkamp and Robert Pires with 20 minutes left and pushed Van Persie forward. Cole punished them, robbing Lauren, cutting inside Sol Campbell and firing home the second, off a post again.
Lehmann tipped Cole's shot on to an upright to prevent a third.
So Chelsea scored their third win over Arsenal this season, two in the Premiership, the other in the Community Shield. The gap between the clubs has grown that wide.