Toronto was trailing 1-0 in the 87th minute when Osorio picked up a lay-off from Jeremy Brockie while charging toward the net and placed a left-footed shot past Crew goalkeeper Andy Gruenebaum for the equalizer.
Then, 4 minutes into stoppage time, Wiedeman slid to meet a looping pass from Bobby Convey and deflected it into the net for the decisive goal.
TFC (3-10-8) snapped a six-game overall skid with the victory and beat Columbus at home for the first time in eight meetings.
Dominic Oduro scored in the 17th minute for the Crew (6-10-5).
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