Abdoulaye Doucoure was Everton’s hero as the French midfielder smashed home from the edge of the box on 57 minutes to spark jubilant celebrations around Goodison Park.
In contrast, Leicester were crestfallen as they went down, despite their 2-1 win over West Ham.
Everton began the afternoon in control of their own fate but put a raucous support of 40,000 fans at Goodison Park through the mill before securing survival.
Scoring goals has been a problem for Sean Dyche’s men and they badly missed the presence of talismanic striker Dominic Calvert-Lewin.
Even when Everton did open up the visitors, Bournemouth goalkeeper Mark Travers produced a stunning save to deny Idrissa Gueye midway through the first half.
The Cherries upset the odds to secure survival weeks ago and refused to lie down and make life easy for the home side.
Marcos Senesi fired inches wide before Yerry Mina needed to make a desperate last-ditch challenge to block Dominic Solanke’s goalbound effort.
Travers was a late replacement in the Bournemouth side after captain Neto missed out for personal reasons and more heroics from the Irish goalkeeper prevented Demarai Gray from opening the scoring early in the second period.
Conceding first would likely have been fatal for Everton, who have not scored more than once at home since October.
The relief was palpable when Doucoure’s sweet strike finally got the better of Travers.
Everton still had an anxious half hour to see out. Jordan Pickford had to make a fine save to deny Matias Vina an equaliser during 10 minutes of added time.
Leicester did what they had to do as the Foxes won for just the second time in 17 games.
But it was too little, too late for a talented squad that badly underperformed this season.
In contrast to Everton, Leicester have an array of attacking weapons and they showed the quality they possess with the opening goal as Harvey Barnes exchanged a one-two with Kelechi Iheanacho and slotted calmly into the far corner.
Wout Faes headed in Leicester’s second just after the hour, but by that point the home crowd at the King Power knew Everton led and needed a favour from Bournemouth that never arrived.
Leeds required a series of results to go in their favour and never gave themselves a chance as Harry Kane opened the scoring after just two minutes at Elland Road.
Pedro Porro doubled Spurs’ lead early in the second-half and Kane reached 30 Premier League goals for the season after Jack Harrison had pulled one back for Leeds.
Lucas Moura rounded off the scoring with virtually his final kick of a five-year Tottenham career.
Victory for Spurs was not enough for secure a place in next season’s Europa Conference League as Aston Villa beat Brighton 2-1 to seal seventh.