The midfielder capped a week in which he made his Scotland return by giving his side a victory which should have been more straightforward following the first-half dismissal of visiting midfielder Tonet.
Jamie Mole put the Tynecastle men in front in first-half injury-time but Billy Mehmet's unlikely equaliser against the run of play ensured Csaba Laszlo's side had to battle all the way for their second consecutive home win.
Stewart missed a second penalty in injury-time at the end of the match and Mehmet screwed a header wide when he should have scored with almost the last touch of the ball as the match reached an exciting climax.
Laszlo handed debuts to new signings Marian Kello, his side's third keeper in as many games, and Uganda international David Obua but he would have hoped for an easier afternoon following Tonet's dismissal.
Hearts were the first to threaten after only three minutes at a sunshine-baked Tynecastle, and it was from the unusual source of left-back Lee Wallace.
The Scotland Under-21 international set off on a marauding run from deep which saw him evade the visiting defence but not Mark Howard as the Buddies keeper blocked Wallace's low effort with his leg.
Stewart opened brightly, clearly buoyed by his return to the international fold with Scotland in midweek when the former Manchester United trainee made his first appearance in dark blue in six years..
His pin-point through ball sent lone striker Jamie Mole scampering away in the inside left channel but his weak effort was knocked away by defender Will Haining after sneaking past Howard.
Stewart then played in Andrew Driver twice in the space of five minutes but the winger could not find the end product that the superb passes deserved, hitting his first effort into the arms of Howard and the next into the sidenetting.
With 17 minutes gone, the Tynecastle outfit came within a whisker of the opener as Laryea Kingston drove a 30-yard effort towards the roof of the net only to see Howard tip it over the bar.
With 25 minutes on the clock, St Mirren's already-tough task of taking something out of the match became more difficult as they were reduced to 10 men.
Spanish summer signing Tonet was initially cautioned in the 24th minute for a late challenge on full-back Jason Thomson on the right edge of the box.
And when, two minutes later, he chopped down Stewart in the centre of the pitch, referee Calum Murray was really left with no option but to hand the midfielder a second yellow card and send him packing.
Hearts pressed with a near-total domination of possession but struggled to find the cutting edge in the final third as St Mirren put up two banks of four to protect Howard's goal.
As the match entered first-half injury-time, however, Mole seized possession 25 yards from goal and fired in the opener past Howard's despairing dive.
Five minutes after the interval the impressive Kingston nearly got the killer second goal Hearts were seeking but his effort from an acute angle struck the near post and bounced to safety.
Visiting boss Gus MacPherson made a bold move 25 minutes from time when he threw on a second striker, Jim Hamilton, for midfielder Garry Brady.
Hamilton's introduction paid immediate dividends as St Mirren grabbed an unlikely equaliser in the 71st minute.
Franco Miranda's free-kick was nodded back across goal by Hamilton and when Murray returned it into the six-yard box Mehmet had the easiest of tasks to knock the ball home.
The goal stunned Hearts but they responded in perfect fashion only four minutes later by going back in front.
Miranda was the sinner, hauling down Driver in the box unnecessarily to give away a penalty.
Stewart stepped up to cap a fine week by drilling low past Howard from the spot.
Howard got the better of his adversary in injury-time as he dived to his left to knock Stewart's second penalty away.
St Mirren poured men forward when they could in the closing stages as they looked for a second equaliser but Hearts hung on for all three points.