The Stars overcame an early two-goal deficit, and then fell behind early in the third period on Clarke MacArthur's third goal of the season.
Dallas forced overtime on a goal from Radek Dvorak with 7:13 to go in regulation.
Jonas Gustavsson stopped all three shootout shots after making 26 saves in regulation and overtime. The loss went to Kari Lehtonen, who stopped 20 shots.
Going into Friday's action Dallas and Boston were the only teams in the NHL without an overtime loss this season. Both teams lost in a shootout Friday.
The Maple Leafs have won two in a row and jumped past Boston into first place in the Northeast Division.
Dallas had a two-game winning streak snapped, but the point the Stars earned pushed them into a tie with San Jose at the top of the Pacific.