Juve headed to Borussia Dortmund's Signal Iduna Park for Wednesday's last 16 second leg tie protecting a slender 2-1 lead from the first leg in Turin.
But just like in that match, Tevez opened the scoring - the former Manchester City man unleashing a rocket 25-yard effort in just the third minute.
Tevez then turned provider after the break to lay on the assist for Alvaro Morata to end the tie as a contest, before rounding off the scoring with his second and completing a 5-1 aggregate victory.
"Tevez is an extraordinary striker," head coach Allegri told Mediaset. "Not only does he score goals, but he also helps his team-mates and the midfield too."
Juve will deservedly draw plaudits for their defensive solidarity and swift counter-attacking football, but Allegri believes his side will have to play better to progress even further in the tournament.
"It's a deserved victory, but we can do even better," he added.
"We can improve in terms of passing and game management. This squad has everything needed to play even better than they did tonight."
