Stewart, one of four candidates on the shortlist for the PFA Scotland Player of the Year award, collected his second yellow card just after the hour mark after he was adjudged to have dived by referee Craig Thomson.
Either side of Stewart’s dismissal, Danny Swanson fired Saints ahead and Iain Davidson put through his own net in a match where chances were few and far between.
A low-key contest finally sprung to life eight minutes into the second half when Brian Graham fed Swanson who netted St Johnstone’s first goal with a low shot into the bottom right-hand corner.
And after Stewart had headed for an early bath, the visitors extended their lead courtesy of Davidson’s own goal on 66.
As the Dark Blues tried to find a way back into the game, former Hibs defender James McPake fired a free kick narrowly wide on 82, while Luka Tankulic went close with a shot from outside the box three minutes from time.
During a dismal first 45 minutes, Swanson blasted an early shot over the bar for St Johnstone whose keeper Alan Mannus saved comfortably from Paul McGowan after half an hour.
And with 44 minutes on the clock, Mannus was again called upon, saving Jim McAlister’s 12-yard header which was travelling towards the top left-hand corner of the net.