Everton registered their first win of the season thanks to Roger Johnson's own goal and a late header from Tim Cahill as they shattered Birmingham's 13-month unbeaten home record with a 2-0 victory.
David Moyes' side moved off the bottom of the table and it was no more than they deserved after dominating possession.
Johnson deflected a low cross from Leon Osman past Blues keeper Ben Foster nine minutes into the second half and, in injury time, Cahill turned in Leighton Baines' cross.
Everton made a promising start and knocked the ball around in confident style with Cahill getting on the end of a deep cross from Baines, but his downward header was collected by Foster.
Aiyegbeni Yakubu dragged a shot across the face of goal as City were pinned back and Cahill could not hide his frustration when heading wide from a Baines centre.
Birmingham did not threaten until the 26th minute as Cameron Jerome poked his shot well wide after a mistake by Sylvain Distin.
Everton were soon back on the offensive and a slip by Johnson left Yakubu with a clear run at goal. But Foster managed to get a hand onto his cross-shot and Liam Ridgewell was behind him to complete the clearance.
Blues fans tried to rally their team after the break but Everton went ahead through an own goal by Johnson after 54 minutes. Osman sent a low first-time cross to the near post and Johnson got to the ball ahead of Foster and could only deflect it into his own net.
City tried to retaliate and appealed in vain for a penalty when Stephen Carr was challenged by Baines. Lee Bowyer had a good chance but went for the spectacular finish and volleyed over the crossbar.
Then in injury time Cahill made it 2-0 when he headed in a centre from Baines.
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