Ronald Koeman registered his first home Premier League win as Everton manager but required the assistance of a Shay Given own goal from a Leighton Baines penalty to achieve it.
The defender's second-half spot-kick rebounded back off the post and the Stoke goalkeeper to secure a 1-0 win which should, on the balance of play, have been far more comfortable.
Nevertheless the victory gave Everton their best start to a season since 2006 and ensured the renewed positivity at Goodison Park continues to grow.
Koeman handed a first Premier League start to new centre-back Ashley Williams, and also winger Yannick Bolasie, but it was a defender at the other end of the pitch who caught the eye.
It was not really a case of trying to stake a claim for a long-awaited England recall in front of new boss Sam Allardyce as Ryan Shawcross has been playing like this, when injury free, for most of the time he has been at Stoke.
His England involvement was apparently over before it began in 2012 when he came on as a 74th-minute substitute in a friendly against Sweden and promptly saw Zlatan Ibrahimovic score a hat-trick to win the game 4-2.
Shawcross believes those 16 minutes ruined his international career as he did not feature again but with Allardyce, a man known for his admiration of no-nonsense defending, now in charge of the national team he could get a second chance at 28, an age when most centre-backs are coming into their prime.
He was beaten by Romelu Lukaku, who still looks well short of form, midway through the first half but had the presence of mind to retreat and hack away the Belgium striker's effort, which appeared to be going wide, when he shot past Given.
Shawcross then deflected Kevin Mirallas' dangerous header into the arms of his goalkeeper and made a crucial interception on Lukaku.
At times it felt like only he stood between the hosts and them running away with the game.
The extra-long legs of team-mate Peter Crouch, who had Stoke's one genuine effort of the first half, came in useful to hack away the ball inches from the goal-line after Williams' header bounced past Given, who tipped over Mirallas' powerful strike from the edge of the area.
Everton's other Belgian forward looks a different player already this season compared to the forlorn, despondent one he was in the final months of Roberto Martinez's reign.
Mirallas was back to his live-wire best with electric pace, driving runs and threatening shots but if there is one criticism of the 28-year-old it is that more often than not there is no final product.
Five minutes into the second half Shawcross was at it again, throwing himself at Lukaku's close-range shot but even the Stoke captain was powerless to prevent Michael Oliver awarding a penalty when Phil Bardsley tangled with Williams from the resulting corner.
Baines resumed spot-kick duties from Lukaku, last season's main taker, but the usually reliable left-back was relieved to see the ball creep over the line via post and goalkeeper.
As the tempo increased Everton's otherwise untroubled goalkeeper Maarten Stekelenburg deflected Marko Arnautovic's shot on to the crossbar and Given palmed away Barkley's strike.
By the time Shawcross did make an error, 13 minutes from time, Allardyce had already departed but Given came to his captain's rescue to save again from Barkley.