The big finish came with some controversy, after an apparently confusing call by referee Mark Geiger that set up the penalty kick. It was not immediately clear whether Geiger called a foul on Toronto's Julius James or a hand ball on Dallas' Adrian Serioux -- but Toronto Coach John Carver said either way his team was robbed.
Toronto (8-12-8) and Dallas (8-9-11) both needed the three points in their pursuit of a berth in the playoffs.
Toronto remains mired in last place in the Eastern Conference while Dallas is fourth in the West.
Cooper -- who now has 18 goals, second best in the league -- scored in the 34th minute Saturday night before scoring the tying goal in stoppage.
Toronto got a goal in the 72nd minute by Marco Velez and another in the 88th minute by Marvell Wynne.