Everton moved eight points clear of the bottom three with their hard-fought win over Crystal Palace.
Idrissa Gueye scored the winning goal four minutes from time after the Blues twice saw their lead eradicated by Roy Hodgson's side.
Vitalii Mykolenko scored his second in as many games to give Sean Dyche the perfect start before Eberechi Eze converted from the penalty spot, after Jarrad Branthwaite tripped the England international.
Abdoulaye Doucoure restored the Blues' lead, only for Odsonne Edouard to pounce on a James Tarkowski mistake.
Defeat for Luton means they remain in the bottom three with Bournemouth leapfrogging them out of the relegation places.
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Stephen KillenAbdoulaye Doucoure has highlighted the momentum that
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