The victory lifts Everton into seventh place in the Premier League standings, just two points behind sixth-placed Chelsea, as they chase a first European campaign in eight years.
In contrast, Chelsea's hopes of securing UEFA Champions League qualification suffered a significant setback, with the defeat marking their fourth in succession across all competitions.
The hosts set the tone early, looking the more energetic side throughout the opening period. Their breakthrough came after a well-weighted through ball from James Garner, who had recently earned his first England call-up. Beto latched onto the pass, beat Wesley Fofana, and delicately chipped Robert Sanchez with the outside of his boot to open the scoring.
Chelsea had opportunities to respond, with Enzo Fernandez forcing a sharp save from Jordan Pickford before the interval, while efforts from Joao Pedro, Moises Caicedo, Marc Cucurella and Fofana were all thwarted by resolute defending.
The visitors attempted to change the momentum after the break, with manager Liam Rosenior introducing Alejandro Garnacho at half-time, followed later by Estevao Willian and Liam Delap.
However, Everton doubled their lead when Idrissa Gueye won possession and surged forward before setting up Beto, whose strike slipped through Sanchez for his second goal of the night.
Iliman Ndiaye then capped off the performance late on, curling a superb effort into the top corner to seal the result.
Pickford produced several key saves to preserve the clean sheet, while Sanchez endured a difficult outing, as Everton made a clear statement in their European pursuit.