The Argentina international, who also scored in Juve's 2-1 victory in the last 16 first leg tie in Turin, caught goalkeeper Roman Weidenfeller off guard in the early stages of Wednesday's contest at Signal Iduna Park.
Tevez then played in Alvaro Morata, also on the scoresheet in Turin three weeks ago, to tap home the second with 20 minutes remaining.
The former Manchester City man drilled home a third in the 79th minute to cap off a fine individual performance and reward Juve's counter-attacking masterclass, as they completed a 5-1 aggregate win.
It was no less than the Serie A champions deserved, with Massimiliano Allegri's men excelling particularly after the break - Weidenfeller twice forced to deny Morata before his goal.
For Juve, progression to the last eight will go some way to silencing the doubters who have voiced claims that they have been largely unable to replicate their domestic form in Europe, on the back of their Champions League group-stage exit in 2013-2014.
The Champions League has provided some respite for a Dortmund side who have struggled for much of the Bundesliga this campaign, and their exit now means that participation in Europe's premier club competition next season is highly unlikely.
Juventus opened the scoring in the third minute in some style.
Tevez collected Morata's pass 25 yards from goal and Dortmund goalkeeper Weidenfeller was late to react as the Argentine striker's fierce effort flew into the left-hand corner.
Having found the goal, Juve seemed content to protect their lead, although Stephan Lichtsteiner also tried his luck from range - Weidenfeller this time up to the task.
The visitors were dealt a blow just before the half-hour mark, when an apparent hamstring injury saw Paul Pogba replaced by Andrea Barzagli.
Dortmund looked more threatening after the Frenchman was taken off, but a series of set-pieces and crosses into the box were dealt with well by Juve's defence - Pierre-Emerick Aubameyang's flashed shot the best the hosts had to show.
The Germans failed to register a shot on target in the first half and they were fortunate not to be 2-0 down five minutes after the restart.
Tevez evaded several Dortmund challenges before slipping Morata in one-on-one, with the Spaniard attempting a deft chip over Weidenfeller that the goalkeeper blocked.
Morata again wasted a great chance to give Juve clear daylight, the former Real Madrid man collecting Roberto Pereyra's ball on the right of the penalty area and forcing Weidenfeller to save with his legs.
The third time proved a charm in the 70th minute, though, as Tevez sprung the offside trap before unselfishly squaring for Morata to provide the tap-in.
And Tevez was celebrating again with 11 minutes remaining, collecting Arturo Vidal's throughball before his angled drive across Weidenfeller nestled in the back of the net to complete a comfortable win.
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