Pirlo slammed home a free-kick from the edge of the area to give Juve a 1-0 win over Fiorentina on Thursday in the second leg of their last-16 tie at the Stadio Artemio Franchi and seal a 2-1 aggregate success.
Italy midfielder Pirlo rescued Juve for the second time in as many games after finding the net with an 89th-minute set-piece in a 1-0 Serie A win over Genoa on Sunday.
And defender Bonucci was quick to hail the impact of the 34-year-old stalwart.
"We knew it was going to be a tough game because they too wanted to keep going in this competition," Bonucci told Mediaset.
"We played with the awareness that we are a great team and the right humility that allowed us to suffer under pressure.
"Plus we have a champion like Pirlo who can turn any game. Those who step on to the field put themselves at the disposal of the side and sacrifice for their team-mates."
Pogba echoed the sentiments of Bonucci, expressing his delight at avenging the 4-2 Serie A defeat Juve suffered at Fiorentina in October.
"We're very happy. We still remember the 4-2 defeat here and it was important for us to overturn that result," Pogba said.
"We said before the match that if we stuck to our usual game plan, the goal would eventually come.
"Pirlo? He's got a golden foot and I need to train for many years if I'm going to be able to shoot like him."
Victory keeps alive Juve's hopes of competing in the final, which will be held at their home stadium in Turin on May 14.
