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.
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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.