The Toffees opened the scoring in the 27th minute when Jarrad Brainthwaite's strike squirmed under Alisson Becker.
Sean Dyche's side survived a period of Liverpool pressure at the end of the first period, before they doubled their advantage courtesy of Dominic Calvert-Lewin's 58th-minute header.
Although Luis Diaz rattled the post, the Reds were unable to claw their back into the contest, ensuring Everton could celebrate their first home victory in a Merseyside derby since October 2010.
After suffering his first defeat at Goodison Park, Jurgen Klopp's hopes of winning a league title in his final season as Liverpool boss are now hanging by a thread.
The Reds are three points adrift of leaders Arsenal, while they are just one point better off than Manchester City, who have two games in hand.
Branthwaite nets crucial opener
The hosts thought they had been presented with an early opportunity to take the lead when referee Andy Madley pointed to the spot after Alisson had brought down Calvert-Lewin.
However, the home faithful's joy turned to frustration as replays showed Calvert-Lewin had strayed into an offside position, denying Everton the chance to go to the penalty spot.
Just over 10 minutes later, James Tarkowski met Dwight McNeil's floated free-kick to nod the ball across goal for Calvert-Lewin to attack, only for Allison to make an instinctive stop to keep the headed effort out.
Everton's relentless pressure ultimately paid off just before the half-hour mark when Branthwaite netted his third goal of the season after Liverpool failed to clear their lines from a free-kick.
The ball kindly broke to the Everton defender, who managed to squeeze his effort under Alisson and over the line.
After getting off to a slow start, Liverpool carved out their first meaningful chance in the 35th minute when Darwin Nunez found himself one-on-one with Jordan Pickford, only to fire his effort at the England international.
As the first half neared its conclusion, Nunez then knocked the ball into the path of Luiz Duiz, who drew a strong stop from the Everton goalkeeper.
Calvert-Lewin doubles Everton's lead
After taking a narrow lead into the break, McNeil lead Everton's quest for a second, with his fierce strike drawing a superb fingertip save from Alisson.
However, there was nothing the Liverpool goalkeeper could do to prevent Calvert-Lewin from scoring from the subsequent corner.
The Everton striker rose above everyone in the box to meet McNeil's deep corner and thump an emphatic header past the Brazilian shot-stopper.
With a two-goal deficit, to overturn, Diaz went agonisingly close to pulling a goal back, only to see his right-foot shot crash against the far post.
Liverpool were ultimately unable to find their best form, and while Harvey Elliott forced Pickford into a late stop, Everton managed to see out the encounter with minimum fuss to claim three precious points.
Despite being hit with an eight-point deduction, the Toffees are on the brink of securing safety with eight points separating them from the bottom three.
As for Liverpool, they could drop down to third position if Man City collect at least a point from Thursday's meeting with Brighton & Hove Albion.
The Reds will have to pick themselves up for Saturday's away clash with West Ham United, while Everton will carry significant momentum into their home game against Brentford.