The home skipper secured three points for his side from the spot in the 23rd minute after Hugh Murray was adjudged by referee Stevie O'Reilly to have handled the ball in his own box when challenging for a high cross.
Christian Nade and David Templeton had chances to increase the lead for Hearts, who have struggled for goals at home this season, but previously in-form St Mirren carried little threat from start to finish.
The win consolidated fifth position for Hearts and kept alive their hopes of breaking into the top four while it brought to an end their visitors' run of victories.
The triumph will also send Csaba Laszlo's men into their Co-Operative Insurance League Cup semi-final with St Mirren next month in good spirits.
Hearts manager Laszlo made five changes to the side beaten by Aberdeen in the Active Nation Scottish Cup last weekend.
Ruben Palazuelos, Nade, David Obua, Jason Thomson and Templeton all returned to the starting line-up with Suso Santana, Ian Black, Rocky Visconte and Gordon Smith dropping to the bench.
St Mirren boss Gus MacPherson replaced Watford-bound Stephen McGinn in midfield with Stephen O'Donnell while Craig Dargo came into the side at the expense of Michael Higdon.
Two of the Hearts players introduced after the poor showing at Pittodrie, Nade and Templeton, were quickly into the action as they combined in the eighth minute to create the game's first opening.
Nade twisted and turned down the right before finding Templeton in the box with a clever cross but the right-winger's header sailed two yards wide.
Laszlo's men were undoubtedly on top in the early stages and, after Templeton forced Paul Gallacher into a fine low save a minute later, Nade then flashed a header of his own just wide.
Templeton in particular looked dangerous every time he was fed the ball by Hearts skipper Stewart, who was controlling central midfield with calm authority.
But it was not a piece of attractive football which gave Hearts the lead as St Mirren midfielder Murray handled the ball when jumping for a high ball in his own box midway through the first half.
Stewart wasted little time in stepping forward to slide the ball into the bottom-right corner and put his side ahead from the penalty spot.
The goal did not change the pattern of the game with Hearts remaining on the front foot and looking a far superior side to the one which surrendered so meekly to Mark McGhee's team last weekend.
St Mirren boss MacPherson was vocal on the touchline in his encouragement of his lacklustre side, who had won their previous three games prior to the trip to Edinburgh.
But the manager's words were having little effect and Obua could have doubled Hearts' advantage just before the break after being set free by Scott Robinson but blasted his effort high and wide.
St Mirren looked busier at the start of the second period but still carried little threat and in fact Hearts centre-half Marius Zaliukas found time to step forward in the 50th minute and test Gallacher with a low drive which the keeper handled competently.
Laszlo's men continued to press for a second and in the 55th minute Nade played Robinson through one on one but Gallacher did well to race from his line and force the striker to take the ball so wide that he could not go for goal.
In an increasingly niggly game, Hearts came close to doubling their lead on 66 minutes when Robinson broke from the edge of his box and cleverly played in Templeton but his cross-shot was saved by Gallacher.
MacPherson made his first change with 20 minutes remaining and it was an attacking one, striker Higdon coming on for midfielder O'Donnell.
The first real moment of alarm in the Hearts box arrived in the 74th minute when keeper Marian Kello failed to collect a fairly aimless high ball but Eggert Jonsson was on hand to clear his lines.
With the visitors showing a hint of a threat, Laszlo decided to make his first alteration when he introduced Smith for hard-working striker Robinson after 78 minutes.
MacPherson also brought on former Hearts star Allan Johnston and Steven Robb for David Barron and Murray with five minutes left in search of an unlikely equaliser while Zaliukas limped off for Hearts to be replaced by Black.
St Mirren also threw defender Chris Innes, a scorer in their last two league games, forward for the five minutes of added time but they failed to even force a save from Kello as Hearts secured victory.