
David Moyes' side had lost their last two league games, but took an early lead through Joleon Lescott, heading in from close range after Middlesbrough had failed to clear a corner.
They went on to keep their first clean sheet of the season, although that was more to do with Middlesbrough's poor finishing than any great defensive work.
South Korea forward Lee Dong-Gook headed against the bar from close range and George Boateng and Gary O'Neil both went close, but Everton sealed the win as Steven Pienaar combined with Mikel Arteta to add a second in the 58th minute.
DPA