Ethan Moreau skated in from the right side and slid a pass across to Stoll, whose a shot hit the inside of the crossbar and dropped into the net.
Rookie Matt Underhill made his first start in goal for Chicago and stopped 29 shots.
Defenseman Eric Brewer had a pair of goals for Edmonton, which d moved within four points of eighth-place Los Angeles in the Western Conference playoff race.
Tyler Arnason had two goals and an assist for the Blackhawks.
Edmonton last won all four games over Chicago in a season series