The Blues inflicted a knockout blow on United's hopes of making a successful defence of the Barclays Premier League and kept their title bid on track with a comprehensive victory at Stamford Bridge.
Jose Mourinho's side moved two points behind leaders Arsenal after Eto'o's hat-trick - his fourth, fifth and sixth Premier League goals of the season - in the victory exposed the numerous shortcomings which leave United 14 points adrift of the summit.
Perhaps more crucial for David Moyes and United, whose reply came from substitute Javier Hernandez, is the deficit to the Champions League qualification places.
Seventh-placed United sit six points behind fourth-placed Liverpool and fifth-placed Tottenham with 16 games remaining after seeing their seven-match unbeaten away run end.
A miserable afternoon was compounded for Moyes and United when captain Nemanja Vidic was shown a straight red card for a reckless challenge on Eden Hazard in stoppage time.
Rafael was fortunate not to follow his skipper in being sent off for a two-footed lunge on Gary Cahill.
Both Chelsea and United are in transition, but it is clear who has more work to do after Mourinho's men claimed a sixth win in seven Premier League games.
Moyes was adamant his side are not a fading force following his appointment as Sir Alex Ferguson's successor; Mourinho, meanwhile, insisted he would never write off United.
If the Portuguese will not, even after extending his home unbeaten Premier League run to 71 games with his 100th win in the competition, most now will.
United's attacking endeavours relied on an 18-year-old Adnan Januzaj and that, coupled with the gaping defensive holes Chelsea exposed, increased the sense Moyes must recruit top-class reinforcements this month to chase a top-four spot.
Should United overturn a deficit in Wednesday's semi-final second leg with Sunderland there may be some solace in the Capital One Cup, but will that be enough to satisfy the likes of Wayne Rooney?
Mourinho has repeatedly insisted Chelsea, and not United, were always his first-choice destination last summer, and was mocked by visiting fans over the Old Trafford link.
The self-proclaimed Special One insists he believes in the Chelsea project, even if he will target a "killer" striker in the summer.
Rooney was the subject of two bids last summer before Eto'o was recruited from Anzhi Makhachkala as a fall-back option and the Cameroonian was preferred to Fernando Torres in a side showing two changes following the win at Hull.
The other was in defence, where Branislav Ivanovic returned earlier than expected from a knee injury, Cesar Azpilicueta shifted to left-back and Ashley Cole was dropped in front of watching England boss Roy Hodgson.
United, with Rooney and Robin van Persie again out injured, made three changes following the win over Swansea - Jonny Evans, Phil Jones and Ashley Young coming in - and began on the front foot.
But the Blues went ahead when Jones backed off Eto'o, whose shot looped up off Michael Carrick's out-stretched leg and into the top corner.
David Luiz, again playing in midfield, was intimidating United physically and was booked for an over-zealous aerial challenge on Antonio Valencia which enraged the United bench.
If Luiz was the enforcer, Hazard's influence as sorcerer was increasing as he found space to run at United.
Januzaj, who could yet team up with Hazard for Belgium, was United's most creative force but no one was in the box to meet his dangerous cross.
Another Januzaj cross evaded John Terry and reached Danny Welbeck, who got a shot away under pressure from Azpilicueta, but Petr Cech saved smartly.
Januzaj then found a rampaging Patrice Evra, whose cross was poor, and Chelsea broke with Willian and Hazard influential on the counter.
Chelsea doubled their advantage when the visitors failed to clear a corner.
Ramires found Cahill on the right side of the area and the defender centred around a static defence for Eto'o to sweep in.
It was a major blow prior to the interval, but the decisive one followed and featured more abject defending.
Cahill was allowed a free header from Willian's corner and David De Gea saved on the line, but Eto'o poked in the rebound.
United, who saw Evra depart injured, threw on Hernandez alongside Welbeck.
The Mexican pulled a goal back 12 minutes from time when he converted Jones' shot after Welbeck's pull-back.
But that was as good as it got for United, who saw Vidic sent off and Rafael booked in stoppage time as Chelsea triumphed.