Toronto (2-7-5) grabbed the lead when a Luis Silva free kick deflected off Woolard's head and past United goalkeeper Bill Hamid, breaking a 1-1 tie.
Robert Earnshaw earlier had scored his team-leading sixth goal of the season as Toronto notched its first road victory of the season.
Dwayne De Rosario netted a penalty-kick goal in the 19th minute for United (1-11-3), which extended its club-record winless streak to 13 games.
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