Everton's goals came courtesy of Richarlison from a James Rodriguez assist, and a well-taken penalty from Gylfi Sigurdsson. That gives Carlo Ancelotti's side their first win at Anfield since September 1999.
So who were the standout performers on the night in Budapest?
✔️ GOOD PERFORMANCE
Jordan Pickford: 8.2
The Everton stopper made numerous saves to thwart Liverpool. The England international made five saves, including a point-blank save from Mohamed Salah at a crucial time in the second half, to keep the reigning English champions at bay.
Pickford commanded his area superbly, and was one of Ancelotti's best performers on the night.
A goalkeeper very much growing in confidence.
❌ BAD PERFORMANCE
Mohamed Salah: 6.4
A disappointing outing from the Egyptian star. Salah produced a listless performance in the first half, and wasted a couple of chances in the second.
Salah found it difficult to get into the game for The Reds, and was well-marshalled by Ben Godfrey and Lucas Digne in his area of the pitch.
Liverpool's No.11 only produced one shot on target in the entire 90 minutes, and only supplied one cross throughout the game for Roberto Firmino and Sadio Mane.
Despite scoring 17 goals this season, Salah's overall performances have dipped, and this was the latest in a string of mediocre displays from the 28-year-old.
Andy Robertson: 6.4
A poor performance from the Scottish left-back. Robertson failed to produce any tangible quality in the final third.
Despite Everton spending the majority of the time in their own half, Robertson only delivered three crosses in the 90 minutes, a low considering his undoubted talent.
The left-back is having a poor season by his own lofty standards, and had another bad outing here.
⭐ STAR MAN
James Rodriguez : 7.2
This was what Ancelotti brought the former Real Madrid player to the club for, to create moments like this.
James has blown hot and cold in his first season in England, but all the inconsistency will be washed away after playing a pivotal role in setting up Everton's first for Richarlison.
The Colombian kept the ball superbly, and took the pressure off of the Everton rearguard by holding the ball, keeping possession, and playing the ball into the channels as the away side hit on the counter.