Everton battled their way out of the relegation zone with a hard-fought 2-1 win against Leicester City after defenders Vitalii Mykolenko and Mason Holgate scored at the King Power Stadium on Sunday.
Frank Lampard's side moved up to 16th position with 35 points, one point above the drop zone, as Leeds slipped to 18th following a 2-1 defeat at Arsenal. Watford and Norwich City have already been relegated this season.
Everton made the most of Leeds' stumble for their first away success in the league since August - against Brighton & Hove Albion.
"It's about the team performance. To win 2-1 away from home – it feels like forever since we won away from home," said goalkeeper Jordan Pickford, who made stunning saves in the second half.
"It's about commitment, attitude, team spirit. That's what gets you over the line."
Everton are hoping to avoid playing in the second tier for the first time since 1954.
Player ratings from the match can be seen in the picture gallery above. To view the next image, click on the arrows or swipe if on a mobile device.