Cenk Tosun and Idrissa Gueye scored in either half as Everton piled the pressure back on relegation battlers Huddersfield with a 2-0 win at the John Smith's Stadium.
Turkey forward Tosun's clinical finish gave Everton a half-time lead and Senegal midfielder Gueye blasted home their second with 13 minutes left.
It was a damaging defeat for Huddersfield, whose victory over Watford in their last match had given their survival hopes a big lift.
A seventh home loss of the season, though, coupled with wins for relegation rivals Crystal Palace, Southampton and West Brom, has left David Wagner's side three points above the drop zone.
Everton have now lost only one of their last seven games, winning four, but their travelling fans made clear their displeasure at the continued presence of Sam Allardyce in their dugout.
Huddersfield were relentless for the opening half hour and were rewarded for their tenacity by wrestling control and enjoying a concerted spell of pressure.
Rajiv van La Parra's appeals for a penalty were waved away by referee Lee Probert after the winger went to ground under Nikola Vlasic's challenge.
Van La Parra then fizzed a first-time shot from Alex Pritchard's pinpoint cutback over the crossbar but, against the run of play, Everton broke free to snatch the lead six minutes before the interval.
Theo Walcott slipped the ball out to Tosun on the right edge of the area after weaving his way into Huddersfield's half and the Turkey forward hit a right-footed shot across Jonas Lossl and into the bottom corner.
Everton spurned a chance to double their lead early in the second half when Seamus Coleman mis-controlled Leighton Baines' free kick in front of goal and his weak effort was gathered by Lossl.
Denmark goalkeeper Lossl denied Coleman again, this time with his feet, as Everton looked to finish off the West Yorkshire side, but Huddersfield, roared on by another sell-out crowd, battled gamely on.
Town boss Wagner sent on Philip Billing and Scott Malone for Collin Quaner and Jonathan Hogg, while Wayne Rooney was left to wait another game at least before his first goal of the year after he was replaced by Tom Davies.
Pritchard swung and missed at a free shot on goal from Van La Parra's cutback as Huddersfield chased a crucial equaliser.
Wagner's last throw of the dice was to send on striker Laurent Depoitre in place of Van La Parra, but Everton struck a second killer goal in the 77th minute.
Substitute Oumar Niasse's cross was teed up by Baines on the edge of the area and Gueye fired an unstoppable right-footed shot into the bottom corner.
Still Huddersfield pressed but Ramiro Funes Mori blocked Depoitre's goalbound shot and Cuco Martina was equally brave to thwart Malone in the closing moments.