The Reds dominated the opening passages of play and could have been ahead when Ashley Young, playing on the left after a spell out with injury, forced goalkeeper Petr Cech into a low save. But United were unlucky in conceding the first goal, when Eto'o eluded Phil Jones to cut in from the right and shot goalwards, the ball hitting Michael Carrick's foot to loop up and over the stranded David De Gea.
David Moyes' men took their time to get back into the game but did carve out more chances before the hammer blow of Eto'o's second. Adnan Januzaj was the main threat, but Danny Welbeck's shot straight at Cech from six yards, having been found by Januzaj, proved telling when the Blues doubled the lead just before half-time.
Ramires collected a cleared corner to feed Gary Cahill on the right, and the defender's cut back was clinically despatched by the Cameroon striker. The break provided little respite for the Reds, who fell three behind when De Gea blocked a Cahill header only for the lurking Eto'o to poke the ball home from point-blank range.
Hernandez provided much-needed spark from the bench, reducing the arrears when diverting Jones' low effort past Cech. But there were no late heroics, only Vidic given his marching orders from referee Phil Dowd in stoppage time, compounding the day's disappointment with an instant three-game ban.