Head Huddersfield Towna Jan Siewert said he was "disappointed but proud" after his team lost to Everton in his first game.
Richarlison scored the only goal from the jump in the third minute after his first kick was saved to lift the pressure on manager Marca Silva after FA Tofees came to Millwall on Saturday.
Everton dropped to 10 men in the last 24 minutes after replacing Lucas Digne with Adam Diakhaby, who was naked.
Aaron Mooy, who returned with seven weeks of injury, had a free-kick shot, Huddersfield's first attempt on target.
The city – which was 11 points behind for safety – pushed the equalizer, but Elias Kachunge's head was saved by Jordan Pickford.
Former Borussia Dortmund Siewert reserve chief said: "I saw why Pickford was number one in England with incredible savings.
"We should not look for excuses, we have to focus on. It's the process that started. I saw many things I did in training.
"The most important thing is to create chances and goals will come. The guys got my ideas and we had a chance."
Huddersfield fails to take their chances
Terriers will condemn their failure to take advantage of their numerical advantage. They dominated the possession in the second half, especially after having dropped off, but have lost 11 of the last 12 games.
Maybe they wonder what could happen that Digne did not crash Diakhaby on the edge of the box forward with a goal – although the Frenchman has not hit Huddersfield yet.
They had 10 hits, the same amount as the Toffees, but shooting was not their problem this season; scoring has. Their conversion rate of 6.84% is the lowest in the Premier League. No other team is a unique person.
They equaled the record for the lowest number of goals after 13 home games – five, with Arsenal 1912-13. There are 13 of them in 24 matches.
Siewert first managed Huddersfield after replacing German Wagner, though he knows that his side will likely be tied to the championship. However, Mooy's return from knee injury will be a welcome boost for the West Side of Yorkshire and he has helped establish a current opportunity with Kachung.
Kachunga had another better header that was professionally rescued, as Huddersfield's chance to score another point came from November.
It's not easy on the eye, but Everton did the job
Chief Tofees Silva desperately needed to win with his side who won eight points in the previous 10 games, which is the third worst race in the division.
And that was before he dumped them out of FA Cup Millwall during the weekend.
They got to win at John Smith Stadium, but they had to level up with less than a star performance.
Richarlison opened the odds after 129 seconds in the second attempt with Tom Davies. Gylfi Sigurdsson left distance from Jonas Loss.
They only managed to shoot the target after a break and had to see the match after Digne was rejected for the rejection of a very clear scoring opportunity. French left-back was in the field for only 11 minutes as a replacement for Leighton Baines, who picked up an injury from his first Premier League since August.
Turkish striker Cenk Tosun, who had a lively first half, replaced young full Jonjoe Kenny while Silva changed shape to make sure his team had only won the third Premier League victory since November.
Midfielder Idrissa Gueye, who had been rejected by Paris St-Germain, missed the match, but Silva for BBC Sport said he had a smaller problem with the odds and no new offer.
"They did nothing more"
Everton boss Marco Silva told BBC Sport: "The main thing was to win, do everything to get three points and give a great response to us and our supporters.
"Three points from home and a clean setup were important to boost our confidence." It was difficult with 10 men who played the match on Saturday, 10 days to prepare, which is deserved for our players.
"One free kick, one header, but they did not do anything anymore. Jordan has gone well in those two moments."
Match statistics – the longest goal of droughts since 2002
- Huddersfield is without a win in the last 11 games with Everton (D5 L6), as he won 1: 0 in March 1956.
- Everton kept a clean sheet in four of his last five games with Huddersfield
- Everton has been undefeated in the past 14 appearances in the Premier League against the sides that start from day one at the bottom of the table (W7 D7), from 2: 1 defeat to Wolves in May 2004.
- Huddersfield did not score 50% of his home league Premier League (16/32) – the highest percentage in the history of the competition
- Huddersfield has now failed to score in each of the last four games – Terriers have gone a long way longer without finding the last part of the net in October 2002 (of five)
- Lucas Digne's red card was Everton's third season in the Premier League – only Leicester (four) saw more players who went to 2018-19.
- Richarlison scored 11 goals in all of Everton's competitions this season, as did Everton's top scorer in all competitions in 2017-18. (Wayne Rooney).
Man match – Mathias Jorgensen (Huddersfield)
Huddersfield faces a tough challenge at Siewert's second game – Chelsea hosts on Saturday (15:00 GMT). Everton is at the same time host to Wolves.