Everton recovered from a strong Queens Park Rangers start to equalise through a Julio Cesar own-goal, leaving the two sides level at the break.
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It was a dream start for Mark Hughes's struggling side as Junior Hoilett ran with the ball from a Cesar punch and his shot from outside the box was deflected past Tim Howard after just two minutes.
It could have been 2-0 on eight minutes. Howard slipped taking a kick and Adel Taarabt found Armand Traore but Bobby Zamora could not connect to his cross.
On 16 minutes Cesar was forced into a decent save from a Nikica Jelavic free-kick.
Ryan Nelsen headed a good chance over the bar for the home side after a dangerous ball was whipped in by Esteban Granero.
Everton were level in the 32nd minute with a huge slice of luck. Silvain Distin's header came back off the post and went in off Cesar.
Two minutes later it was almost 2-1 Everton, Phil Jagielka this time rattling the woodwork from a Leighton Baines corner.
Taarabt and Granera combined well just before half-time but Jagielka was alert to glance the danger clear.