The Cameroonian punished the champions to keep the pressure on his side's title rivals, while David Moyes' men fell to their seventh league defeat of the season despite a late consolation strike from Javier Hernandez.
Chicharito pulled a goal back for United after coming off the bench, but it was another miserable afternoon for Moyes, who will also now be without his captain Nemanja Vidic for a spell after he was sent off in injury time for a wild challenge on Eden Hazard.
Defeat saw Moyes' side beaten for the first time away from home in the league for almost four months, as its chances of retaining the title collapsed.
The champions are 14 points behind Arsenal and now face a battle to even qualify for the Champions League, sitting six points adrift of fourth-place Liverpool.
Jose Mourinho has no such problems, as he celebrated his 100th Premier League win in only 142 games — requiring less matches than any other manager to achieve the landmark.
United made an encouraging start, but the club found itself behind after 16 minutes when Eto'o conjured up a goal out of nothing.
There appeared to be no danger when the striker picked up a loose ball, but he cut in from the right and jinked past Jones before unleashing a shot from the edge of the penalty area that deflected off Michael Carrick and looped into the far corner of the net.
United responded well to going behind and the lively Adnan Januzaj created a great chance for Danny Welbeck when he picked out the striker in the area, but the England international's tame finish was saved by Petr Cech.
That miss proved to be costly too, as Gary Cahill picked out Eto'o a minute before halftime and the Cameroon international finished from 6 yards out.
Eto'o then made United pay for some poor defending just three minutes into the second half to complete his treble. He was first to react when Cahill's header was well saved by De Gea, with the alert striker on hand to tuck home the rebound.
Welbeck's frustrating afternoon continued when he headed wide from close range, but substitute Hernandez did pull a goal back when he turned in Jones' shot from inside the 6-yard box 12 minutes from time.
It was too little, too late for Moyes' side though, and Nemanja Matic came on to make his second debut for Chelsea five minutes from time after the club from Benfica as the Blues saw out the victory with ease.
United’s misery was compounded when Vidic was then shown a straight red card for a cynical challenge on Hazard, while Rafael was lucky to escape with just a yellow after lunging at Cahill.