Cenk Tosun and Idrissa Gueye struck the goals which gave Sam Allardyce's side victory to leave the Terriers just three points clear of the relegation zone.
And with David Wagner's side facing clashes with Manchester City, Chelsea and Arsenal in their remaining fixtures they are now anxiously looking over their shoulders at Southampton and Stoke.
Crucially, Saints have a better goal difference than the Yorkshire side, so if they make up thew three point difference that will be enough to move them above Huddersfield.
Huddersfield knew this game was vital to their chances of ensuring top flight football for the second successive season.
But they were outfought and seen off comfortably by an Everton side who are now safe in eighth in the table despite the unhappiness with manager Allardyce.
Allardyce's position in charge at Goodison Park has been in doubt with the supporters unhappy at the style of football being served up by the former England boss.
And despite him claiming he is staying for another season in the build-up to this match, the fans still made their feelings known with a banner demanding he leaves his job.
But on the pitch they at least had plenty to cheer, with Tosun's first half goal putting them in control of the match.
Huddersfield desperately needed to find a way back into the game in the second half, but they found little on offer from the well marshalled Everton defence.
And when Gueye lashed home the second goal midway through the second half, any hopes of a comeback were ended.
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