Manchester City assumed pole position in the title race with a 3-2 win, but Everton gave the conspiracy theories short shrift after Manuel Pellegrini's side endured a testing time at Goodison Park.
Anything other than a City victory would have handed the initiative back to Liverpool, but three points put them top of the table on goal difference with Chelsea to play today and the Reds tomorrow night.
If they win their remaining two matches at home to Aston Villa and West Ham, City cannot be caught irrespective of what their rivals do in their final two fixtures.
Everton, despite many fans claiming they would be happy to lose in order to help stop their near-neighbours' title bid, needed a win themselves to stay in the hunt for the Champions League, but defeat handed fourth spot to Arsenal 24 hours before they play.
City manager Pellegrini insisted, however, the chase to the finish line is not over, saying: "The worst thing we must do is think that today we finished the Premier League.
"We have to play Aston Villa and West Ham who are not fighting for anything, they can play without pressure. We must try to win our last two games at home, then we will see what happens."
Sergio Aguero's goal and two from Edin Dzeko settled the game at Goodison, with Everton having opened the scoring through Ross Barkley and later pulling one back through Romelu Lukaku.
Any questions about Everton's appetite for the win was answered brilliantly in the 11th minute. Barkley showed just why England coach Roy Hodgson should take him to Brazil this summer with a strike which would have graced any World Cup.
Leighton Baines and Steven Naismith combined down the left to tee up the 20-year-old who hit a sublime first-time shot from 25 yards which flew past goalkeeper Joe Hart and into the top corner.
Then came one of those moments when fate seems to play a significant part. All the intimations from Aguero were that he could not continue with an apparent groin problem, but while City were readying his replacement Toure slid through an inviting pass and the Argentinian's predatory instincts took over as he skipped past Antolin Alcaraz to beat Tim Howard at his near post.
Everton switched from their experimental 3-4-2-1 formation to 4-1-4-1 to try to combat the loss of control but whether the changes affected the defence or not Dzeko's free header for City's second - after he had almost beaten Howard at his near post again - came far too easily.
Barkley remained Everton's one driving force and a powerful run from halfway just after the break set up Naismith one-on-one with Hart only for the goalkeeper to tip his shot around the post. It was a pivotal moment as City went straight down the other end and Fernandinho picked out Samir Nasri who crossed for Dzeko to sidefoot home.
Lukaku, badly out of form, then popped up in the 65th minute to head home a Baines cross to make it 3-2.
Roberto Martinez replaced Phil Jagielka, making his first appearance for 10 weeks, with Gerard Deulofeu as they went for the win to keep alive their Champions League hopes.
And his weaving run and shot was deflected into the side-netting and with it went their faint hopes of a top-four finish.