The result ended Everton's impressive nine-match unbeaten run in the Premier League and strengthened the Reds' grip on the top spot, where they currently lead second-placed Arsenal by a commanding 12 points.
Reds boss Arne Slot admitted the clash was no walk in the park. "It was hard-fought, no doubt about it," he said after the match.
"Everton have been tough to break down—nine games unbeaten, barely conceding goals or chances. They defend deep with 10 men around their box, and with players like James Tarkowski and Jarrad Branthwaite, crosses are pointless, they head everything away.
"They're a threat on the counter too, with Beto up top. Every set-piece, every throw-in, you've got to be switched on, and that's what makes them so tricky."
The game lived up to its billing as a classic derby scrap. Everton's physicality was on show early when Tarkowski clattered into Alexis Mac Allister with a high challenge inside the first 10 minutes.
Despite a VAR review, the centre-back escaped with just a yellow card, a decision that left Slot bemused but tight-lipped. "I won't add much," he said. "Even people who don't support Liverpool have said it was clear what should've happened. Was I surprised? No."
Everton had their moments to stun the home crowd. Beto thought he'd scored in front of the Kop in the first half, only for an offside flag to deny him.
Minutes later, the striker broke free again, this time onside, but rattled the post after Abdoulaye Doucoure's pinpoint pass. Everton boss David Moyes, still winless in 19 trips to Anfield as a manager, rued those misses. "We had big chances," he said post-match. "You don't get many here, and we needed to take them."
Liverpool, though, turned the screw after the break. Jota, who'd been denied by a block in the first half, seized his moment on 57 minutes. Latching onto a loose ball, he danced into the box and smashed it home, sending Anfield into raptures.
"I'm delighted for him," Slot said. "He was close early on, but they're so strong defensively. For him to find that space and finish, it was massive for us, the team, the staff, and the fans."
The Reds nearly doubled their lead late on when Luis Diaz saw a shot cleared off the line by Tarkowski, who redeemed himself after his earlier escape. Everton, boosted by the return of Iliman Ndiaye from injury, pushed for a leveller but couldn't breach Liverpool's backline.
The hosts held firm, stretching their unbeaten league run to 26 games and cementing their place at the Premier League summit, 12 points clear of Arsenal.
Slot praised his side's persistence. "We got Diaz one-on-one with their full-back so many times, 10, 15 maybe, and that's what you need against a side like this," he said. "You keep going, hoping one chance falls, and it did with Diogo."
For Everton, it was a first defeat in 10 league outings, while Liverpool celebrated a vital three points in their title charge.
The Merseyside bragging rights, for now, belong to the Reds, who are setting a relentless pace at the top.