After Martin Skrtel put the Reds in front from close range at Stamford Bridge after only four minutes, Hazard hit back in the 17th with a superb strike. Eto'o gave Jose Mourinho's team a decisive lead from Oscar's back pass in the 34th.

Third-place Chelsea trails leader Arsenal by two points and Manchester City by one point. Liverpool is six points adrift after slipping to a second consecutive loss.

Hazard was splendid throughout in his playmaker role, while Chelsea's defenders did a good job of containing Luis Suarez, who was reunited with Branislav Ivanovic for the first time since he bit the Serbian defender on the arm last season and was banned for 10 games.

"The kid is giving everything," Mourinho said about Hazard. "He was a very talented player, but he was a kid enjoying football in a funny way. Now he understands his responsibilities. I'm so happy with the kid."

Mourinho also accused Suarez of showing his "wild nature" and simulating after the striker protested he should have been given a penalty when Eto'o obstructed him in the box in the second half.

"Suarez lost a duel with (Cesar) Azpilicueta, Azpilicueta has the ball and is leaving the box with the ball and now he's doing an acrobatic swimming pool jump to try to get the penalty," Mourinho said. "When the situation is like this and you are losing comes the nature of the player, the wild nature of the player or the cultural nature of the player."

With captain John Terry becoming the fourth Chelsea player to make 600 appearances for the club, the game started at a high tempo, with both sides involved in a gritty contest for possession.

After Eto'o was lucky to escape a booking for his challenge on Jordan Henderson, Liverpool made the most of the subsequent free kick, with Skrtel scoring a poacher's goal from close range. Chelsea failed to clear Philippe Coutinho's free kick, Suarez headed the ball beyond Ivanovic and Skrtel tapped it home.

Chelsea reacted immediately, only for Hazard to see his effort saved before Gary Cahill headed wide from Frank Lampard's free kick in the eighth minute.

Chelsea's penalty appeals were waved away by referee Howard Webb after Hazard appeared to be clipped by Lucas in the box, and Lampard forced keeper Simon Mignolet to tip the ball over with a trademark powerful shot from outside the box.

The home side was rewarded for its pressure soon afterward when Hazard gave Mignolet no chance with a superb curling shot for his eighth league goal of the season.

Mourinho was forced to make an early defensive change as the injured Ivanovic was replaced by Ashley Cole after 30 minutes. But Liverpool struggled to contain the Blues' relentless attacks and Eto'o converted his team's dominance into a goal when he scored from close range from Oscar's pass, despite Mignolet getting a hand to the ball.

The Reds continued to threaten on the break and had a chance to level before the interval, with Joe Allen's shot from the right side of the box drawing a good diving save from Petr Cech.

There were further scoring chances in the second half, with Liverpool defender Mamadou Sakho unlucky to see his looping header hit the crossbar from a free kick as Cech looked well beaten. At the other end, Eto'o missed a clear-cut chance when he fired straight at Mignolet from a good position in the 54th.

Suarez's volley four minutes later was easily stopped by Cech as Liverpool created more space in the hosts' half.

But Chelsea weathered Liverpool's attacks and could even have won by a bigger margin. Former Liverpool striker Fernando Torres eased past Mamadou Sakho and Skrtel but failed to beat Mignolet with his shot in the closing stages.

"Christmas Day eating our turkey we were top of the league. A few days and games later we're fifth. I think that's the way it will go between now and the end of the season," Liverpool manager Brendan Rodgers said. "I think it's brilliant and it makes it really exciting."

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