Jozy Altidore struck a brace for Toronto as they came from behind to win 3-1 at Vancouver Whitecaps, while fellow debutant Robbie Findley also scored.
The MLS' highest-paid player - Sebastian Giovinco - created Altidore's first goal, while former Marseille midfielder Benoit Cheyrou was involved in the build-up for Findley's strike.
With Toronto having never won silverware in their eight previous seasons in MLS, the Canadian club's fans had plenty to be impressed about with Vanney's new-look squad.
The match did not start well for the visitors, however, with Vancouver's Uruguayan striker Octavio Rivero converting a one-on-one opportunity in the 19th minute to score on his MLS debut.
But Toronto were level just after the half-hour mark, with Giovinco threading a pass into the box to Altidore, who finished from a tight angle.
Vanney's men hit the front in the 59th minute with Cheyrou receiving Michael Bradley's pass in Toronto's forward half, before releasing full-back Justin Morrow down the left.
Morrow's cross was slotted into the net by Findley.
Toronto's third goal came thanks to a penalty, with Whitecaps defender Pa Modou Kah hauling Altidore down in the box and the United States international produced a panenka from the spot.
In Dallas, the home side edged out San Jose Earthquakes thanks to a stoppage-time goal from veteran striker Blas Perez.
A long-ball into the penalty area in the 92nd minute was partly cleared by San Jose's defence but Moises Hernandez's follow-up shot was nodded into the net by Perez.
DC United and Houston Dynamo also picked up 1-0 wins at home to begin their respective league campaigns, accounting for Montreal Impact and Columbus Crew respectively.
Saturday's other two games ended scoreless with Philadelphia Union and Portland Timbers held at home by Colorado Rapids and Real Salt Lake respectively.
