Seamus Coleman, Michael Keane and Anthony Gordon were all on target as Everton eased their relegation worries.
The win moved 16th-placed Everton to 22 points, five clear of the drop zone. Leeds are a point ahead in 15th, having played a game more.
Everton came out firing and could have gone ahead through Gordon after a minute but the youngster was denied by a last-ditch tackle from Luke Ayling, before Coleman made their early pressure count, finishing off an intricate team move with a diving header at the far post in the 10th minute.
Leeds' early troubles were compounded by a calf injury to left-back Stuart Dallas, who was forced off and replaced by Leo Hjelde.
The visitors, however, almost grabbed an equaliser against the run of play in the 18th minute when Rodrigo's dipping effort from distance struck the bar, but Everton continued to drive forward and doubled their lead through Keane five minutes later.
The centre back towered above Pascal Struijk to meet Gordon's outswinging corner for his second league goal of the season.
Leeds made two changes at the break, bringing on Tyler Roberts and Adam Forshaw for Raphinha and Mateusz Klich, but barely troubled Jordan Pickford, failing to hit the target despite seeing more of the ball.
"It was a fair result," said Leeds manager Marcelo Bielsa. "They attacked better than us. In the second half we defended a little bit better but we couldn't manage to attack."
Gordon wrapped up the points in the 78th minute when Richarlison's left-footed effort from the edge of the area took a slight deflection off him before squeezing past Illan Meslier.
Substitute Salomon Rondon could have made it four right at the end after being played in by Dele Alli but his shot from 12 yards out was smartly tipped over by Meslier.
"If you watch the game you will see it was difficult for us to anticipate their forwards," added Bielsa, whose side are now winless in their last three league games.
Everton boss Lampard was delighted with the result, calling it an "incredible afternoon".
"It was nice. What we did today was something special in terms of the performance. It showed an attitude, aggression and work rate," he said.
"Relief is three points and the table looks slightly better this week but I'm just so proud of the performance. I haven't seen a performance like that in the first half... that has made me really happy. We need to build."