10-man Everton held on at the John Smiths Stadium to deny Jan Siewert a dream start as Huddersfield Town boss.
Richarlison's early strike was enough for the Toffees, who saw Lucas Digne sent off in the second-half.
The pressure on Marco Silva has somewhat eased after their first win in two matches.
Image via Premier League
It was a nightmare start for Siewert in the Huddersfield dugout. Richarlison's shot was blocked but the striker pounced and poked home the rebound.
Perfect start for Everton and the under-pressure Marco Silva - but a "welcome to the Premier League" goal for his opposite number.
Image via Premier League
Huddersfield were showing signs of improvement in their first game under Siewert especially when the second-half started.
Adama Diakhaby was through on goal before being taken down by Digne, who was sent off for Everton.
From the resulting free-kick, Aaron Mooy struck a free-kick and it was brilliantly saved by Jordan Pickford.
The Everton goalkeeper was on hand again to deny a Huddersfield equaliser. This time, Elias Kachunga's effort was well-saved.
The Toffees just about held on for the three points. It was a spirited performance from the Terriers - but not enough for a first point as Huddersfield boss for Siewert.
The Managers
Huddersfield Town head coach Jan Siewert: "I saw why Pickford is England's number one with incredible saves.
"We shouldn't find excuses. We need to focus. It's a process which has started. I saw many things I implemented in training.
"The most important thing is we create chances and the goals will come. The lads got my ideas and we had chances."
Everton boss Marco Silva: "The main thing was to win, to do everything to get the three points. And to give a big answer to ourselves and our fans.
"Three points away from home and a clean sheet was important to boost our confidence. It was difficult with 10 men, having played a game on Saturday. They had 10 days to prepare. It was well deserved for our players.
"One free-kick, one header, but they didn't create anything more. Jordan did well in those two moments."