Everton inflicted a humiliating 4-0 defeat on Manchester United, who have now lost six of their last eight games.
Out-fought and out-played by their hosts at Goodison Park, United didn't manage to produce a shot on target until the 85th minute.
Sky Sports pundit Gary Neville was outspoken in his criticism of United's display while Jamie Carragher described it as the worst he had seen from United during his time at Sky Sports.
An acrobatic volley from Richarlison put Everton ahead in the 12th minute and the hosts were two up at half-time courtesy of Gylfi Sigurdsson's 25-yard drive (28).
Lucas Digne fired home a third (56) early in the second half, and Theo Walcott raced clear to complete the scoring in the 64th minute.
Courtesy of their fine victory, Everton are up to seventh in the league table while United's latest defeat leaves them two points outside the Champions League places with just four games remaining.
WATCH: Neville condemns United performance
How Everton dismantled Man United
Everton started the game brightly and it took a sharp reaction save from David de Gea to deny Richarlison early on.
The goal came soon enough though as Dominic Calvert-Lewin flicked on Digne's long throw and Richarlison was waiting, six yards out, and connected sweetly on the stretch to send the volley high into the net.
Everton: Pickford (7), Coleman (7), Keane (7), Zouma (7), Digne (8), Gueye (8), Schneiderlin (7), Richarlison (8), Sigurdsson (9), Bernard (7), Calvert-Lewin (7).
Subs: Walcott (7), McCarthy (6), Jagielka (6)
Man Utd: De Gea (5), Lindelof (5), Jones (4), Smalling (5), Dalot (6), Matic (4), Fred (5), Pogba (5), Rashford (6), Martial (5), Lukaku (5).
Subs: Young (5), McTominay (5), Pereira (6)
Man of the match: Gylfi Sigurdsson
The Blues pressed for a second and found it after a rare United attack. Having easily dealt with a corner, Everton countered, the ball was worked to Sigurdsson, and he cut inside and drilled his shot into the bottom corner with De Gea slow to react.
Solskjaer made a double change at the break, sending on Ashley Young and Scott McTominay, but it made little difference and Everton extended their lead 11 minutes into the second half.
Marco Silva made two changes to the Everton team that lost at Fulham with Michael Keane and Morgan Schneiderlin coming in for Phil Jagielka and the suspended Andre Gomes.
Meanwhile, Manchester United brought in Diogo Dalot, Nemanja Matic and Romelu Lukaku for Ashley Young, Scott McTominay and Jesse Lingard.
Sigurdsson's corner was punched clear by De Gea, but Digne was waiting on the edge of the box and arrowed a half-volley into the corner of the net. The ball was past the goalkeeper before he could move.
The Goodison Park faithful was jubilant and they had more to cheer eight minutes later. Sigurdsson was involved again, sliding a through ball into the path of substitute Walcott with the United defence nowhere to be seen.
Despite a heavy touch, Walcott had plenty of time recover and slip the ball past De Gea into the far corner.
The result was beyond doubt, and it took until the 85th minute for United to muster a shot on target. Solskjaer and his side have little time to reflect on a fifth successive away defeat before they host Manchester City on Wednesday, while Everton will now be optimistic of finishing seventh and potentially claiming a Europa League spot.
Gary Neville: "I'm furious, to be honest with you. I've often said about clubs in the last seven years, if you've got weeds in the garden then you've got to get rid of them. But there is some Japanese knotweed at that football club and it is attacking the foundations of the house and needs dealing with properly. That performance today was rancid."
Jamie Carragher: "That was the worst performance from a Manchester United team I have seen since I have been working for Sky."
Graeme Souness: "That was a team in their armchairs - not a team trying to qualify for the Champions League. It was a team that was plodding, drifting, and going through the motions."
Man of the match - Gylfi Sigurdsson
The Everton No 10 was involved in everything for Everton, scoring the second with a superb strike was distance and setting up Walcott for the fourth, while it was his corner that was punched out to Digne for the third as well. He enjoys playing United, too. He's now been directly involved in nine Premier League goals against them (five goals, four assists), more than versus any other club.
- This was Everton's biggest margin of victory over Manchester United in any competition since October 1984, when they beat them 5-0 in a top-flight contest. It was also Man Utd's biggest defeat to any opposition since October 2016 against Chelsea in the Premier League (also 0-4).
- This was Manchester United's fifth consecutive away defeat across all competitions, their longest such run of losses since March 1981 under Dave Sexton (also five).
- Manchester United have conceded 48 Premier League goals in 2018-19, their highest ever tally in a single season in the competition and their most in a league campaign since 1978-79 (63).
- Everton have won more Premier League points at home to the "big-six" clubs this season (10 - P6 W3 D1 L2) than any other team from outside the top six in the table, with only Man City (15), Liverpool (13) and Chelsea (11) earning more overall at home to such opposition.
- Manchester United have gone 11 consecutive matches without a clean sheet in all competitions for the first time since December 1998.
Everton travel to Selhurst Park next Saturday to take on Crystal Palace in a 3pm kick-off.
Meanwhile, United welcome neighbours Manchester City to Old Trafford on Wednesday, live on Sky Sports Premier League and Main Event, for a crucial game in the title race. Coverage begins at 7pm ahead of an 8pm kick-off.