Tim Cahill celebrated his return to Everton's starting line-up with the winning goal against Stoke at the Britannia Stadium.
Cahill had missed the start of the season with a broken metatarsal that blighted him for much of the last campaign.
But he marked his surprise inclusion by striking the decisive blow, heading home Mikel Arteta's corner in the 76th minute.
Everton looked like they would cruise to victory when goals either side of half-time from Yakubu and Victor Anichebe put them firmly in the driving seat.
But Stoke showed grit, and aided by the potent weapon of Rory Delap's long throw they fought back and restored parity through Seyi Olofinjana and Phil Jagielka's own goal.
However, they were denied what looked like an unlikely point when Cahill had the final word.
Since Stoke moved from the Victoria Ground to the Britannia Stadium 11 years ago, their new home has become renowned for its passionate atmosphere and the stadium was bouncing again at kick-off.
The noise level of the home support was raised another notch in the second minute in anticipation of a trademark lonng throw from Delap, but the ball landed on the roof of Everton's net.
The game's first chance arrived after 12 minutes following a flowing Stoke attack.
The ball was worked out to Liam Lawrence on the right wing and he slid a pass through to Ricardo Fuller, whose low, first-time shot across goal was pushed out by a strong Tim Howard hand before being smothered by the American at the second attempt.
A sloppy passage of play ensued as both teams struggled to retain possession, seemingly becoming bereft of ideas when in the opposition's final third.
New signing Segundo Castillo would not have impressed his team-mates, or the Everton supporters, when he twice misplaced a routine pass and kicked the ball out of play on the half-hour mark.
Another long throw from Delap presented Olofinjana with a shooting opportunity 10 minutes before the break when Everton could only clear the ball to the edge of their own area, but the former Wolves midfielder wildly blasted over the crossbar.
Five minutes later Yakubu put Everton ahead with the Merseysiders' first shot on target of the first half.
A clever reverse pass by Arteta to Cahill created confusion inside the Stoke penalty area. Cahill laid the ball into Yakubu's path and he coolly steered it into the bottom corner from 18 yards out for his third goal of the season.
Five minutes into the second half Everton doubled their advantage through Anichebe.
Arteta won a free-kick 25 yards out on the right of the area.
The diminutive Spaniard took the kick himself, curling the ball with his right foot into the box where Anichebe's glancing header to the far post left Thomas Sorensen rooted to the spot in the centre of his goal.
But Everton's two-goal lead last just three minutes before it was halved by Olofinjana.
Delap's long throw was punched downwards by Howard and the ball deflected into the path of Olofinjana, who volleyed powerfully past the keeper from just beyond the penalty spot.
Stoke thought they had equalised just before the hour when Fuller outmuscled Joseph Yobo on the edge of the area to get to Dave Kitson's flick header.
Fuller took the ball around Howard, tapped into an empty net and wheeled off in celebration, but referee Alan Wiley adjudged that he had fouled Yobo.
Stoke were level in the 62nd minute when another throw launched into the box by Delap flicked off the head of Jagielka at the near post and beyond Howard.
Stoke were fortunate not to concede a penalty when Leon Cort handled the ball inside the box under pressure from Yakubu in the 74th minute.
The offence clearly took place inside the area but Wiley awarded a free-kick on the edge.
The decision incensed David Moyes so much that the Everton manager was sent to the stands following his protests.
Moyes would have felt a sense of justice done two minutes later when Cahill's run to the near post was not tracked by the Stoke defence and he headed home the winning goal.