Dougie Hamilton and Sean Monahan also scored for Calgary, which completed a three-game sweep against Chicago during the regular season. The Flames improved to 14-5-5 on the road.
Alex DeBrincat and Patrick Kane scored for Chicago. The Blackhawks dropped to 2-5-2 in their past nine contests and fell to 12-11-3 on home ice.
Stone flicked a wrist shot from the top of the right circle to notch the decisive goal. Johnny Gaudreau helped to set a screen in front of the crease, and the puck sailed into the top left corner of the net for Stone's third goal of the season.
Monahan gave Calgary a two-goal lead when he scored an empty-net goal with 1:51 to go.
Kane punched in his team-leading 21st goal with seven seconds remaining to close the gap to 3-2.
Flames goalie Mike Smith stopped 34 shots to improve to 22-15-6. On the opposite end of the rink, Blackhawks goaltender Jeff Glass turned aside 20 shots.
Chicago opened the scoring on a power play 3:35 into the first period. DeBrincat fired a wrist shot through traffic from the top of the right circle for his 19th goal of the season and his fifth in the past five games.
Calgary evened the score at 1 at the 1:10 mark of the second period. Hamilton scored his ninth goal during a two-on-one break. Blackhawks defenseman Duncan Keith tried to block the pass across the crease but could not react in time.
The Blackhawks believed that they had gained a 2-1 lead less than three minutes later, but after a lengthy video review, officials waved off a goal by Ryan Hartman because of goaltender interference.
Both teams traded quality scoring opportunities during a back-and-forth start to the third period. Flames center Mikael Backlund missed a golden opportunity when Glass slid across the crease for a kick save. Minutes later, Blackhawks center Jonathan Toews hit the crossbar during an odd-man rush.
--Field Level Media
Calgary | Chicago | |
Johnny Gaudreau 3 | Points | Alex Debrincat 1 |
Johnny Gaudreau 1 | Goals | Alex Debrincat 1 |
Johnny Gaudreau 2 | Assists | Artem Anisimov 1 |
N/A | Power Play Goals | Alex Debrincat 1 |
N/A | Short Handed Goals | N/A |
Mike Smith .944 | Save Percentage | Jeff Glass .909 |
Mike Smith 34 | Saves | Jeff Glass 20 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Calgary | 23 | 3 | 0-4 | 4-5 | 12 | 31 |
Chicago | 36 | 2 | 1-5 | 4-4 | 10 | 32 |