Drogba scored toward the end of each half to give him 10 goals in nine games against Arsenal, while defender Thomas Vermaelen turned the ball into his own net at rain-soaked Emirates Stadium.
"We are playing really well with great team spirit and we need to continue this,´´ Chelsea captain John Terry said. "We soaked up the pressure, and going forward the midfielders and attackers were exceptional.´´
On Saturday, second-place Manchester United maintained pressure on Chelsea by beating Portsmouth to go four points on third-place Tottenham.
After a second straight loss, Arsenal is a point further behind for the fourth Champions League spot, with Liverpool two points behind after Joseph Yobo´s own-goal and Dirk Kuyt´s late strike settled the 212th Merseyside derby at Everton.
Also Sunday, Lee Bowyer scored in the third minute to give Birmingham a 1-0 victory over Midlands rival Wolverhampton, which is in the relegation zone.
In Spain, Zlatan Ibrahimovic scored four minutes after coming on as a substitute, and Barcelona beat Real Madrid 1-0 in the highly-antipated Spanish "clasico´´ match.
Moments after Barcelona´s defense had denied a Gonzalo Higuain effort, Daniel Alves found Ibrahimovic at the far post with a lofted cross in the 56th minute and the Sweden striker never broke stride as he volleyed past Iker Casillas with his left foot.
Roberto Soldado scored a hat trick Sunday to lead Getafe to a 5-1 win over Xerez in the Spanish league, while Athletic Bilbao beat Almeria 4-1. Tenerife rallied to draw 3-3, Deportivo La Coruna won 1-0 at Racing Santander and Osasuna defeated Zaragoza by the same score.
Barcelona leads the standings with 30 points, overtaking Madrid on 28.
In Italy, Diego Milito converted a late penalty to extend Inter Milan´s lead in Serie A with a 1-0 win over Fiorentina on Sunday, while second place Juventus lost 2-0 at Cagliari.
Milito struck five minutes from the end after being brought down by Gianluca Comotto.
For Cagliari, Nene opened the scoring in the 30th minute that gave Juventus goalkeeper Gianluigi Buffon no chance, and Alessandro Matri added a second from a counter attack.
Inter leads with 35 points and Juventus is second with 27. AC Milan, which was due to play Catania later Sunday, is third with 25, one point ahead of Sampdoria.
Also Sunday, it was AS Roma 2, Atalanta 1; Bari 2, Siena 1; Chievo Verona 1, Palermo 0; Lazio 0, Bologna 0; and Parma 1, Napoli 1.
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