The veteran Italian struck deep into injury time at the Juventus Stadium to condemn rivals Torino to a 2-1 victory and extend the Serie A champions' winning run at home in the league to 25 matches.
Vidal had opened the scoring from the penalty spot 15 minutes in only for a stunning solo goal from Bruno Peres to level matters, before Juve were reduced to ten men when Stephan Lichtsteiner was dismissed 12 minutes from time.
However, Pirlo came to Juve's rescue with a powerful late drive to keep the champions three points clear at the top of Serie A, with Vidal paying tribute to the 35-year-old.
"He's an incredible player and only he could have scored that goal," the Chilean explained.
"It was a difficult game, as it always is when we play against them. Torino were fairly defensive-minded and put 10 bodies behind the ball, so it wasn't easy to move the ball around quickly.
"We needed to wait for the right moment to break forward."
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