Tevez’s stunning long-range strike gave the Italians an early lead before the Argentine presented strike partner Alvaro Morata with a simple finish to double the advantage in the second half.
Dortmund’s hopes of progression were in tatters but Tevez added a final flourish, driving home his second and Juventus’ third late on to seal a 5-1 win on aggregate.
The German side gave themselves a good chance of progression after taking an away goal from a narrow 2-1 defeat in Italy a fortnight ago, but the hosts were second best throughout at Signal Iduna Park.
Their prospects suffered a heavy blow within just three minutes as Tevez received possession 25 yards out and unleashed a stinging shot that flew past Roman Weidenfeller and into the top left-hand corner of the net.
The early breakthrough seemed to knock the home side’s confidence and Juventus almost doubled their advantage after the quarter-hour mark when Stephan Lichtsteiner again tested Weidenfeller with an effort from distance, but this time the Dortmund goalkeeper was able to punch the swerving shot clear.
Dortmund gradually established a foothold in the contest but struggled to convert possession into chances. Apart from set-pieces, Jurgen Klopp’s men were restricted to optimistic shots from range.
Juventus eased through the rest of the first period and Morata should have wrapped up the tie early in the second when he was twice sent clear, but on both occasions he failed to beat Weidenfeller, who was quick to close down the shots.
The Spaniard made no mistake in the 70th minute, however, as Dortmund’s defence was caught out by another ball over the top and as Weidenfeller rushed out, Tevez generously slid the ball across for the young striker to side-foot into an empty net.
Dortmund’s misery was compounded nine minutes later when Tevez latched onto Arturo Vidal’s neat pass and he slammed the ball home to wrap up an excellent individual display and seal his side’s place in the last eight.
BORUSSIA DORTMUND: Weidenfeller, Papastathopoulos, Subotic, Hummels, Schmelzer (Kirch 46), Kampl, Bender (Ramos 64), Gundogan, Reus, Mkhitaryan (Blaszczykowski 63), Aubameyang.
JUVENTUS: Buffon, Lichtsteiner, Bonucci, Chiellini, Evra, Vidal, Marchisio, Pogba (Barzagli 27), Tevez (Pepe 81), Pereyra, Morata (Matri 78).
Referee: Milorad Mazic (Serbia).