Sean Dyche expressed his relief after Everton earned their first three points of the season through a Dwight McNeil brace at Goodison Park.
The hosts conceded early as Marc Guehi put Crystal Palace a goal to the good after 10 minutes, as Everton were again undone following a set-piece.
But a fine second-half display from McNeil saw two excellent finishes carry Everton over the line.
It was the first time this season Dyche's side had managed to maintain a lead, with the Toffees having dropped points from winning positions in their last three Premier League matches.
Following news of a possible takeover for the Merseyside club this week by The Friedkin Group, who also own Roma, Dyche was relieved to secure his first victory of the season, and just a sixth league win of 2024.
"I'm delighted for the players, they worked very hard to change a scoreline around," the Everton manager told BBC Sport.
"You know there’s been question marks over many things, and of course, there's been a bit of relief there for me today and relief for the players, and that’s a human thing.
"There's a lot of demand here that we put on ourselves, and we have to answer to that and I thought we did today. We certainly did enough to win the game and that’s what was important."
Everton are yet to keep a clean sheet in the Premier League this season, though Jarrad Branthwaite's return from injury was a major bright spot.
And the Everton defence did look stronger despite a shaky first-half display. The visitors accrued an expected goals (xG) total of just 0.85 from 17 shots.
"It was a bit of nervousness. When you haven’t got that first win you feel nervous. Then you go 1-0 down, the stadium becomes awkward for the players," Dyche explained.
"I spoke to them in the second half about being someone who makes a difference. It’s every person that counts, not just one."
Everton proved far more clinical thanks to McNeil's long-range effort on 47 minutes. They finished on 0.91 xG from just eight shots.
"I thought the feel of the second half was better, not just the quality. Dwight popping up with two goals for two different reasons and some good energy in our play and the big moments went for us today," said Dyche.
Crystal Palace also had the better share of possession with 59.4%, a source of disappointment for boss Oliver Glasner.
"Over 70-75 minutes we controlled the game, but you must be focused all game. It is a big strength of Everton's in set-plays. They do it well and we defended it most of the time really well," he told BBC Sport.
"We tried everything, we changed the system, brought on all our offensive players. They defended with 10 players around their box so we didn't have a lot of space so it was difficult.
"Today we couldn't score the equaliser. If you concede two goals it's not so easy to get a point or to win."
It leaves the visitors without a win in their last six games in the Premier League.
"We know it when we look at the table. Maybe it is a welcome back to reality. Maybe we were flying too high after a great finish to the season. The Premier League is a fight," Glasner added.
Alonso hails Leverkusen rearguard after stubborn Bayern display
Xabi Alonso was proud of his Bayer Leverkusen players after they produced a resolute defensive performance to earn a 1-1 Bundesliga draw at Bayern Munich.
After Robert Andrich gave Leverkusen the lead, Bayern's Aleksandar Pavlovic levelled with a stunning half-volley from 25 yards out which gave goalkeeper Lukas Hradecky no chance.
Bayern, who had won all four of their previous league games under Vincent Kompany, had 18 shots to Leverkusen's three and almost 70% of the possession.
That is the fewest shots Leverkusen have attempted in any of their 98 competitive matches under Alonso, while they also generated just 0.07 expected goals (xG) to Bayern's 1.32.
Despite their lack of attacking threat, Alonso was delighted with his side's defensive resilience, saying: "The energy and belief at Bayern is different to last season, they are going full throttle with and against the ball.
"That was very tough today. We can be happy with the point. I needed more energy from the team.
"I'm happy with that. We were ready to suffer and we did that. We need the discipline and passion of the players.
"It wasn't easy, we didn't have control of the ball. It was a challenge to defend. The point is important... The whole team did very well. We hardly had a chance to breathe but I'm very proud of my players."
Leverkusen midfielder Granit Xhaka, who provided the assist for the opener, said their main strategy was to be compact and deny Bayern opportunities to score.
"We are self-critical. If you score three goals every game, that's not enough. If we play well today and switch gears, we can do something," Xhaka said.
"Defensively, we put in a good performance. The goal today was to be compact and concede little. You can certainly do more with the ball and everyone knows that we can do more. If someone had told us before the game that we would get a point, we would have taken it."
Leverkusen will next turn their attention to the Champions League, when they host AC Milan on Tuesday.
Motta defends Juventus talisman Vlahovic after Genoa brace
Juventus boss Thiago Motta lashed out at those criticising striker Dusan Vlahovic after he scored twice in the Bianconeri's 3-0 win over Genoa on Saturday.
Juve continued their fine start to life under Motta with a routine victory at the Stadio Comunale Luigi Ferraris, Vlahovic netting twice before Francisco Conceicao added a late third.
They have kept a clean sheet in each of their first six matches of a Serie A season for the very first time, also scoring at least twice in five of their last eight games, having done so only once in their previous eight.
Despite Juve's strong run of form, Vlahovic has attracted criticism from some quarters.
Only Christian Pulisic (six) and Marcus Thuram (five) have bettered his four goals in Serie A this term, though, with the Serbian also helping himself to a brace versus Verona.
Motta heaped praise upon Vlahovic after the win, also hailing his defensive work as he said: "No goals conceded is a team effort.
"Scoring goals starts well with [goalkeeper Mattia] Perin and not conceding goals starts with Vlahovic.
"We have a group that wants to defend to have the ball and recover it. This is very important, a team must be solid to aspire to something great."
Motta then added: "Honestly, I think you pay too much attention to a single player. He has always been very good.
"I understand the expectations and needs of a striker at this level. But as I said from the beginning, he is a positive leader who helps a lot.
"I am happy because he scored but I was also happy when he didn't. He must improve and be more connected with the team because he is an important player in many aspects of our game. He is fine and must continue to work as he is doing".
Vlahovic, who has more games with multiple goals than any other player across the last six Serie A seasons (19), said: "The most important thing is that we won and we want to continue like this.
"It's no problem, people talk. If you score you're the best, if you don't you're the worst. It's up to me to respond on the pitch and I will certainly do so.
"Sometimes there are fewer opportunities. People expect me to solve the games and that's normal, I don't run away. I always do everything 100%.
"I'm super calm and I will always give my all on the pitch. For a striker when you don't score it's difficult, but today we won and that's the only thing that matters."
Kompany hopes Kane injury against Leverkusen is 'nothing serious'
Vincent Kompany is hopeful Harry Kane's knock is nothing serious, after the Bayern Munich striker limped off during the 1-1 draw with Bayer Leverkusen.
The England captain, who did not register a single shot during the game, was injured in a collision late on at the Allianz Arena, where Aleksandar Pavlovic cancelled out Robert Andrich's earlier effort.
The stalemate saw Bayern drop their first points of the Bundesliga season, while they turn their attention back to the Champions League with a trip to face Aston Villa in midweek.
Whether Kane features at Villa Park remains to be seen, but Kompany hopes his forward is fit for a return to England.
"I'm not a doctor, but I hope it's nothing serious," the Bayern boss told Sky Sports. "It's still early to say. Hopefully, he'll be fit for Wednesday."
Although Bayern's 100% start to the league campaign is no more, Kompany saw plenty of positives in his side's display.
"As a Bayern coach, you always want to win," he added. "But the performance was as we'd hoped. The counter-pressing was positive, we won the second balls, we created so many chances.
"Normally, in such a game, you don't create many chances, but we did. It was a top game, but there are still many games to go. We just have to keep going."
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