Chelsea have beaten Manchester United to close the gap on Premier League leaders Arsenal to two points.
United started strongly and were nearly rewarded with the opening goal. Ashley Young was played in just inside the box, but his low shot was pushed away by Petr Cech.
The Blues struggled early on and Ramires drove towards goal, but his tame effort was held by David de Gea.
However, the home side took the lead with just over 15 minutes played. Eto'o was given space on the edge of the box and his left-footed strike came off Michael Carrick and into the net.
David Moyes's men responded well and continued to attack despite conceding, with Patrice Evra firing wide from outside the box. Adnan Januzaj played a ball across the face of goal, but no-one was there to tap home.
With the first half nearing its conclusion, Danny Welbeck could have equalised for the away side. Januzaj's cross found the striker, but his shot was straight at Cech.
Eto's deflected shot then floated towards Oscar, who fired over with an overhead kick. However, it was 2-0 a minute before half time.
United failed to clear from a corner, which allowed Eden Hazard to drill a low cross into the box where Eto'o was waiting to fire past De Gea.
With the second half just three minutes old, Eto'o grabbed his hat-trick. Gary Cahill's header was saved and the Blues striker tapped in from close range.
After that Chelsea started to push their opponents back and United struggled to find their rhythm.
However, the visitors created a rare chance when Welbeck got in front of his man from a corner, although his header flashed wide.
They managed to pull a goal back through Javier Hernandez. Phil Jones hit a shot from the edge of the area and the Mexican striker diverted it in from close range.
However, the day got worse for Moyes when Nemanja Vidic was shown a straight red card for chopping down Hazard in stoppage time.