Everton just about clung onto their Champions League dream after largely disappointing in a 1-0 win over already-relegated Derby at Goodison.
Derby threatened first on six minutes when Tim Howard could only palm out Sterjovski's 18-yard shot, but there was little to get excited about in a low-key opening.
Everton should have gone ahead in the 17th minute when Yakubu scooped Leighton Baines' cross over the bar but it was a rare foray forward.
Manuel Fernandes and Hossam Ghaly exchanged half-chances before half-time but the breakthrough did not come until the 56th minute when Leon Osman ran from deep before lashing a fierce 18-yard effort past Roy Carroll.
Emanuel Villa should have equalised in the 64th minute but the striker fired weakly at Howard's legs and Everton held on for the win that leaves them three points behind Liverpool.