Juve’s victory sealed a 5-1 win on aggregate in the last 16 tie as Tevez and Morata, who had each scored in the 2-1 first-leg win, again did the damage in Dortmund.
Tevez weighed in goals either side of Morata’s second-half effort.
Just as he had done in Turin, the 31-year-old Tevez gave his side an early lead with a breath-taking strike to catch out the Dortmund defence.
The Argentinian then beat Dortmund’s off-side trap with 20 minutes left to give Morata a simple tap-in to put the Old Lady in the last eight.
Tevez added his second and Juve’s third nine minutes later when he took Arturo Vidal’s pass and fired home to break Borussia hearts.
“The team played really well, I just do my job and the team deserved the win,” said Tevez.
“We showed our experience and I think we’re on the right path.”
Massimiliano Allegri’s Juventus simply had too much experience for a Dortmund side struggling with confidence issues after a dire start to their Bundesliga season which had left them bottom of the table in February.
“We are all very disappointed. We had planned more, but did not get going,” said Dortmund goalkeeper Roman Weidenfeller.
Juventus also maintained their impressive record at Dortmund with their fourth straight win at Borussia’s Westfalenstadion to go into Friday’s draw.
Dortmund, the 2013 finalists, join Schalke and Bayer Leverkusen in exiting the Champions League at the last 16 phase leaving Bayern Munich as Germany’s sole representative in the quarter-finals.
Dortmund’s task became that much harder with just three minutes gone when Tevez launched a fierce strike off his right foot unmarked from 30 metres out.
It powered past Weidenfeller and left Dortmund needing to score at least twice.
With 15 minutes gone, defender Stephan Lichtsteiner forced Weidenfeller into another save as the Italian league leaders kept up the early pressure.
Allegri was forced into an early change on 27 minutes when defensive midfielder Paul Pogba came off clutching his hamstring made way for Italy’s Andrea Barzagli.
Dortmund chased the game and dominated possession, but Juve stood deep frustrating the hosts’ constant attacks as it remained 1-0 at the break.
Borussia boss Jurgen Klopp brought on Oliver Kirch for injured left-back Marcel Schmelzer at the start of the second half.
Only a good save from Weidenfeller on 50 minutes stopped Juve going 2-0 up when Tevez charged through the Dortmund defence, but the Borussia goalkeeper blocked Morata’s shot.
Just six minutes later Weidenfeller denied Morata again as the Spanish forward threatened to add to his first-leg winning goal.
It finally came on 70 minutes when Tevez sprinted onto a ball over the Dortmund defence, drew Weidenfeller and unselfishly squared for Morata.
Tevez put the result beyond doubt when he added his sixth Champions League goal of the campaign 11 minutes from time with another strike which gave Weidenfeller no chance.