His powerful 20-yard strike, a bolt from the blue, was enough to extend the club’s top-flight stay to a 70th successive season but for long periods that proud record appeared in doubt.
But Doucoure’s 10th goal for the club capped a remarkable turnaround in four months for the Mali international who was training on his own in January after a fall-out with former manager Frank Lampard.
Five days after having his contract extended by 12 months – and with his side just over half-an-hour from heading into the Sky Bet Championship – he delivered when it mattered most and in a way the club can never adequately repay him for.
But it still required a clearance from Conor Coady under his own crossbar and a good save deep into 10 minutes of added time from Jordan Pickford to keep them safe after it initially looked like the Cherries’ second-choice goalkeeper Mark Travers would play a key role in sending the Toffees down.
The home side had started the most significant day in their 145-year history two points outside the drop zone but with Leicester winning at home to West Ham they were heading for only their third relegation and first since 1951.
Then, their top-flight exile lasted three years and the nightmare scenario was that there had been little to suggest over the last couple of seasons another absence would have been any shorter.
Everton had been in the last-day, last-chance saloon twice before in 1994 and 1998 but on both of those occasions their fate was not in their own hands.
In 1994 they beat Wimbledon 3-2 – coming back from 2-0 down – with rivals Ipswich, Sheffield United and Southampton faring worse and four years later they bettered Bolton’s result at Chelsea to survive.
But the stakes seemed much higher on this occasion, and with a new 52,000-capacity stadium at Bramley-Moore Dock due to open for the 2024-25 season this was potentially the last Premier League game at Goodison Park.
However, they are not out of trouble as the club have posted losses in excess of £430million over the last four years and have an outstanding Premier League charge for breaching profit and sustainability rules.
But for now survival, and the relief that brings, is enough.
The men outside of them, however, were midfielder James Garner and winger Dwight McNeil and while the former coped relatively well on his side’s right flank, McNeil, more accustomed to running forward, struggled to cope with David Brooks going the other way.
Up front, winger Demarai Gray found it tough adapting to the central role as, unable to hold up the ball, he resorted to trying to win cheap free-kicks but it was a ploy referee Stuart Atwell regularly saw through.
Gray, who had an early rising drive just over, also found being a striker tough in terms of his positioning as when Doucoure drilled a cross into the six-yard area, he was 10 yards too deep waiting for a cutback on the edge of the box.
Travers, only in the side due to Neto’s absence due to personal reasons, then came to the fore as he tipped over Idrissa Gana Gueye’s powerful strike, parried another long-ranger from the Frenchman and then clawed away Garner’s looping shot in first-half added time.
In recent home games around the half-hour mark, Everton’s initial fire had burned out and opponents claimed the upper hand but on this occasion it was bad news from the King Power Stadium which took some of the wind out of their sails.
Gray’s weak close-range header being scooped away by Travers six minutes into the second half only increased the sense it was not going to be Everton’s day until Doucoure smashed home a drive after a weak header dropped to him.
Crucial interventions from on-loan Wolves and former Liverpool defender Coady and then Pickford from substitute Matias Vina saw them scrape home and sparked the inevitable pitch invasion after relegation was avoided for the second successive season.