Arsenal suffered a setback in their bid to win the Premier League title after slipping to a shock 1-0 defeat at Everton on Saturday.
James Tarkowski's second-half header was enough for Everton to seal a crucial win in Sean Dyche's first game as the club's new manager.
- Stream on ESPN+: LaLiga, Bundesliga, more (U.S.)
Mikel Arteta's side missed out on the chance to go eight points clear of second-placed Manchester City after losing only their second league game of the campaign.
The result also sees Everton climb out of the bottom three as they look to avoid being relegated from the Premier League for the first time in their history.
Tarkowski, who Dyche signed when he was at Burnley, said he hoped the win could help change the prospects for Everton, who had only won three league games all season before Saturday.
"It has been tough for us and the fans and for all the staff in the club. Hopefully this is the turning point for the club, there is a lot of talent here," he told BT Sport.
"It's taken me a while, I need to score more. What a great time to do it and a great day. It's back to work on Monday and we crack on.
"We've lacked that little bit of grit at times and that's what the fans want. We've seen what it's all about today."
Everton started the game brightly and made it difficult for Arsenal to find their rhythm early on.
However, the league leaders had the first big chance after 30 minutes when Eddie Nketiah blasted over from close range.
- Arsenal fail physical test as Dyche makes instant impact
The game came to life after that as Calvert-Lewin came agonisingly close to tapping home from Amadou Onana's cross while Abdoulaye Doucoure's close-range header went wide.
Moments later, Bukayo Saka saw his fine effort blocked off the line from Conor Coady and minutes before the break, Calvert-Lewin's looping header missed the target.
Everton continued their fine form in the second half and took the lead after 59 minutes when Tarkowski headed home from Dwight McNeil's corner.
Arsenal responded to the goal with Leandro Trossard forcing Jordan Pickford into a good save while Saka blazed over from inside the box.
Oleksandr Zinchenko had a decent chance to equalise late on but his shot went over the bar.
The hosts managed to hold on to claim their first victory in the league since October.
Everton winger McNeil added: "We know how good they [Arsenal] are as a team, but we also know how good we are as a team as well with all the chances we had."