Teenager Christian Hernandez scored the match winner three minutes from the end and the visitors' evening was further soured when Dutch defender John Heitinga saw red in injury time for a second caution.
Defeat was tough on Everton, who will complete their brief tour against DC United on Saturday, with striker Jermaine Beckford spurning their best chance after a clever ball from the impressive Mikel Arteta.
Early exit: Johnny Heitinga (right) was sent off for Everton just before the end
Spanish midfielder Arteta pulled the strings for large spells of the match and was unlucky with a free-kick into the side netting.
The Toffees face DC United on Saturday before heading home to take on Oxford United next Friday and Birmingham the following day.
David Moyes' side will have further tests against foreign opposition - Werder Bremen on August 2 and Villarreal on August 5 - before kicking off their Premier League campaign at Tottenham on August 13.
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