Rooney's goal was the only moment of note in a boring opening period.
"There was one player in an Everton shirt today who from the first second to the last second was comfortable on the pitch", the Everton boss said.
Everton are still looking to sign Swansea's talisman Gylfi Sigurdsson, who have valued the Iceland global at £50m. Everton have been busy too, bringing in Jordan Pickford, Michael Keane, Wayne Rooney, Sandro Ramirez and Davy Klaasen.
Idrissa Gueye then saw a tame shot from distance comfortably saved by Butland but chances were few and far between as the Blues toiled to make inroads into a predictably well-drilled Potters defence.
Rooney dropped deeper into midfield in a bid to spark his team into life and immediately began to control the tempo, drawing a booking for Allen when he wriggled clear of the Stoke midfielder, who responded with a blatant tug.More news: Philadelphia Eagles Trade Jordan Matthews To Buffalo Bills
More news: Google engineer fired for 'sexist' memo takes legal aim at company
More news: 'Shep, It Appears To Be a Very Large Chicken'
But in his first Premier League outing Rooney not only scored the victor with a beautifully executed header from a Dominic Calvert-Lewin cross, but he also exuded quality and composure throughout.
Sprinting towards the crowd in delight, Rooney slid to the turf to celebrate before he was mobbed by jubilant team-mates.
That gap of 4,869 days is the longest between goals for the same club in the Premier League.
Calvert-Lewin almost doubled Everton's lead when he robbed Zouma and cut into the penalty area for a drive that Butland pushed away.
Manager Mark Hughes says Saido Berahino, whose fitness was questioned last season, is "in great shape".
Would you like to place a soccer bet?