Leicester, who had taken five points from their last three matches, have 30 points with three games left, falling to 18th place below Everton and Nottingham Forest who both won later.
Fulham never really looked to be in danger with Leicester playing catch-up throughout the contest after a dismal first-half display, which was criticised by playmaker James Maddison.
"Big game for us and we were not at it. We were not hungry enough to want to win the game. We need to do the basics well," Maddison told the BBC.
"We can't defend like we did, that is why we are where we are but it not just the defence, it is the team. The team needs to be watertight and that comes from the front too.
"They played through us. They scored three goals in the first half and it left too much to do."
Leicester face Champions League-chasing Liverpool and Newcastle United in their next two games.
Fulham were gifted the opener in the 10th minute by a howler from goalkeeper Daniel Iversen, who misjudged the trajectory of a Willian free kick and could only watch as the ball bounced past him and into the back of the net.
Leicester's sole attacking outlet in the first half was the ever-lively Jamie Vardy, who twice tested Bernd Leno from range.
The hosts continued to press forward, with Carlos Vinicius squeezing a shot past Iversen in the 18th minute before Cairney scored either side of halftime to give the West London club a four-goal advantage.
Leicester pulled a goal back as winger Harvey Barnes fired into the roof of the net in the 59th minute before Vardy won and missed a penalty, but Willian wrapped up a one-sided victory by curling home Fulham's fifth from distance.
The visitors scored through Barnes and Maddison late on but they merely added some respectability to the scoreline on an awful day for Dean Smith's team.
Marco Silva's Fulham have now won 14 league games this season -- equalling a club record in the Premier League.
"Great moments of football, great goals. The way we played from the first minute was really good," Silva told the BBC.
"We prepared well for the game and the players executed the plan very well. We clearly deserved the three points and it should have been much more comfortable. That is something for us to work on and keep improving."
Fulham remain 10th in the table.
Excellent Everton blitz Brighton with shock 5-1 win
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Everton's Dwight McNeil in action before Brighton & Hove Albion's Jason Steele scores an own goal and Everton's third - Premier League - Brighton & Hove Albion v Everton - The American Express Community Stadium, Brighton, the UK - May 8, 2023. (Photo: Action Images via Reuters) |
Abdoulaye Doucoure scored a brace of first-half goals as relegation threatened Everton produced a masterclass in counter-attack football with a surprise 5-1 Premier League victory at Brighton & Hove Albion on the same day.
Brighton goalkeeper Jason Steele scored an own goal and Dwight McNeil added two more as Everton cut their hosts apart with lightning quick breaks, and then absorbed intense pressure in the second half, eventually conceding when Alexis Mac Allister netted for the home team.
The Merseyside club moved to 32 points from 35 games, two points clear of the drop zone, as they seek to avoid a first relegation since 1951, while Brighton’s hopes of European football next season were dented and they sit in seventh with 55 points from 33 games.
Everton had 23% possession in the game, but were excellent in breaking down Brighton attacks and flooding forward on the counter, scoring 10 percent of their Premier League goals this season in a dream first half.
"It's massive. We started on the front foot, we had a game plan and we stuck to it. We were all brilliant today and we deserved the three points," McNeil told BT Sport.
"We couldn't have got off to a better start. It's a credit to the lads, we've been in a difficult position this year. Now we've just got to build on this game.
"It's massive confidence now, this is about us kicking on as a team. We have a massive game on Sunday (at home to Manchester City) and then two massive games after that."
Doucoure’s first came after 34 seconds as he tapped home from close range, finishing off a low cross after being set up by the excellent Dominic Calvert-Lewin.
Another quick Everton break saw McNeil cross for Doucoure to net a superb second with an excellent volley from 12 yards.
McNeil’s low cross was then directed into his own net by Steele, before the Everton winger added two more in the second half, also from quick counter-attacks.
Brighton manager Roberto De Zerbi made four changes at halftime and his positive move made for a vastly improved home team after the break, but despite being camped around the Everton box, they managed only one goal through Mac Allister.
"Still three cup finals and we have to keep going. You have to take a lot of positives from that," Everton goalkeeper Jordan Pickford said.
"The gaffer (Sean Dyche) made a couple of changes. We set the standard early. We have to keep going as a group, the togetherness is there but we mustn't take the foot off the gas."
