The Mali international rose well above his marker to make no mistake from Danny Higginbotham's perfect cross after some fine work by substitute Michael Tonge.
Stoke's victory was deserved on the balance of play, but Filipe Teixeira will be kicking himself for blazing high and wide after picking Andy Griffin's pocket in the 80th minute.
City suffered an early blow when record signing Dave Kitson was stretchered away with a leg injury and replaced by Richard Cresswell in the 11th minute.
But they almost took the lead just a minute later with a tremendous effort by Sidibe.
He controlled a long ball on his chest before flicking it over a defender and unleashing a vicious volley which Scott Carson tipped acrobatically for a corner.
Carson, who turned down Stoke to join Albion in the summer, was booed every time he touched the ball by the home fans, who preyed on his mistake for England in midweek.
Ishmael Miller finally landed a blow for the visitors in the 29th minute when his 18-yard volley dipped too late to trouble Thomas Sorensen, with the ball landing on the roof of the net.
But Stoke continued to enjoy the better of a low quality contest, forcing Albion to defend a succession of corners and the long throws of Rory Delap.
The loss of suspended top scorer Ricardo Fuller was an obvious blow for the home side as they lacked a real spark in the final third.
Stoke tried to up the ante at the start of the second half and Tom Soares squandered the best opportunity of the game in the 51st minute.
The trickery of Cresswell opened the door, but Soares shot too close to Carson from 14 yards and the rebound was booted to safety before Sidibe could pounce.
Tonge replaced Soares in the 65th minute and his first piece of the action ended with a swerving shot which Carson gathered at the second attempt.
But Albion were defending well, particularly under Stoke's aerial bombardment, with Abdoulaye Meite and Jonas Olsson holding firm until Sidibe settled it.
Albion have now failed to win at Stoke in 17 attempts in a record that stretches all the way back to 1982.