The Potters looked set to make it 10 league games without a win until the 84th minute when the veteran striker turned in a knock-down from a corner to sink the club he left last summer.
It was Stoke's first league win in 10 attempts and has given their play-off hopes a boost, while Wednesday remain in the relegation zone.
Just after the half-hour mark the first bit of quality play saw Powell cleverly slip Brown into a shooting position, but the winger's effort was easy for Wednesday goalkeeper Keiren Westwood.
Angus Gunn made similarly-light work of a Rhodes header as the visitors countered, and Bannan crashed a direct free-kick into the Stoke wall before the end of a desperately drab first half.
Potters pressure early in the second half saw Westwood palm a Powell effort for a corner from point-blank range.
On the hour mark, Powell's reverse pass sent Brown into space and he cut the ball back for Fletcher, but a brave block from Lees denied the former Wednesday man.
Westwood clawed an Allen cross to safety as the home side started to dominate, and the ex-Liverpool midfielder steered a great chance the wrong side of the post after being teed up by Brown.
Wednesday, who had won three of their previous four matches, struggled to get sight of Gunn's goal and their frustration was evident when Rhodes ballooned a cross from a dangerous position for a throw-in.
But the breakthrough finally came late on when Fletcher reacted quickest in the box following a Tommy Smith cross to stab home from close range.
Substitute Sam Clucas almost made it safe but his late header was well saved by Westwood.
Gunn held a Rhodes header in injury time as Stoke held on for their first win since December 19.