With Dallas captain Brenden Morrow in the penalty box for interference, Hossa fired a one-timer from the slot past goalie Kari Lehtonen after receiving a nifty, behind-the-back pass from Patrick Kane.
Patrick Sharp had a goal and an assist for the Blackhawks, who improved to 4-0 and matched the franchise's best start set during the 1972-73 season. Corey Crawford made 21 saves and stopped Ryan Garbutt on a penalty shot.
Chicago's high-powered offence, which racked up 14 goals in the previous three games, needed the man-advantage to score all three Thursday night.
Part of that was due to an outstanding performance by Lehtonen, who made 38 saves after coming within 3.4 seconds of a 39-save shutout Tuesday in a 2-1 win at Detroit.
The Stars had a prime opportunity to win when Niklas Hjalmarsson's tripping penalty with 1:18 left in regulation gave them a chance to end it on the power play. But even though the man-advantage carried over into overtime, they were unable to capitalize.
Ray Whitney's second goal of the season midway through the second period gave Dallas a 2-0 lead, but the Stars continued to get into penalty trouble, allowing three goals on their last four trips to the box.
Loui Eriksson put the Stars up 1-0 with a short-handed goal on a spectacular effort with 1.4 seconds remaining in the first period. He fought his way around defenceman Brent Seabrook at the Chicago blue line and fired a wrist shot that Crawford initially appeared to stop, but the puck came loose and slid just over the goal line.
Less than 4 minutes into the second, and just seconds after Lehtonen's sparkling pad save on Marcus Kruger's backhander, Garbutt was pulled down from behind by Seabrook on a breakaway. Garbutt was awarded his first career penalty shot, but Crawford made a glove save on his backhand attempt.
Chicago continued to pepper Lehtonen with shots, but the Finnish netminder made impressive stops on Toews, Brandon Saad and Hossa.
Following a turnover by Michal Rozsival, Whitney found himself alone in front and his point-blank backhander over Crawford's shoulder gave Dallas a two-goal lead at 10:41.
The Blackhawks finally solved Lehtonen on a power play at 15:57 when Sharp attempted a pass through the crease that was inadvertently deflected in by Dallas defender Trevor Daley.
Dallas nearly scored another last-second goal at the end of the second when Alex Goligoski's slap shot slithered through Crawford as the final seconds ticked off the clock, but Chicago defenceman Duncan Keith cleared it off the goal line as the buzzer sounded.
NOTES: During the game, the Stars announced that they signed restricted free agent centre Jamie Benn to a five-year contract worth $26.25 million. ... The last time the Blackhawks opened the season with at least three straight victories was back in 1972-73, when Hall of Famers Tony Esposito and Stan Mikita led them to a 4-0 start en route to the Stanley Cup final. ... Dallas entered having allowed one goal during 5-on-5 play through its first three games. ... Kane's two assists extended his scoring streak to four games (two goals, five assists).