Carlos Tevez scored twice as Juventus sealed a 5-1 win on aggregate in the last 16 tie as he and Morata, who had each scored in the 2-1 first-leg win, again did the damage in Dortmund.
Just as he had done in Turin, Tevez gave his side an early lead with a breath-taking strike to catch out the Dortmund defence.
After setting up Morata for a tap-in on 70 minutes, Tevez added his second and Juve’s third nine minutes later when he fired home Arturo Vidal’s pass.
The result means Italian league leaders Juventus join Atletico Madrid, Barcelona, Bayern Munich, AS Monaco, Paris Saint-Germain, Porto and Real Madrid in Friday’s last eight draw.
“There are no easy teams. But if we play like we did tonight we’ve no reason to fear anyone,” said Morata.
“It was a really impressive display. We defended when we needed to and struck when we had the chance to attack.
“It was a difficult game but the entire team tackled it in an incredible manner.”
Morata singled out Tevez for praise after the 31-year-old beat Dortmund’s off-side trap to give the Spaniard a simple tap-in to put the Old Lady in the last eight.
“It’s a dream to play with Tevez. When I was a youngster I watched him on the TV and now he sets me up to score goals,” beamed Morata.
Juventus coach Massimiliano Allegri was delighted with this side’s display over the two legs.
“The most important thing for me tonight is the confidence we have shown,” said Allegri.
“We delivered a big technical and physical performance, we have been doing our work in Italy since the start of the season, but now we are doing it on the European stage.
“We put in two great matches against Dortmund and we deserve to go through.
“It doesn’t matter who we now meet at this level whether its Barcelona, Munich or PSG.”
– ‘A game to forget’ –
Dortmund coach Jurgen Klopp admitted the 2013 Champions League finalists had failed to bow out of this year’s competition in style having barely threatened the Juve goal.
“That was a game to forget, the early goal we conceded was the worst that could have happened,” said Klopp.
“Juve were not only clever, they played some really good football.
“We hardly got into good shooting positions.
“Every minute the opponent gained in confidence and we ended up having none.
“Juve were simply better than us, but they also had the perfect start after three minutes.
“We were too harmless. If you don’t shoot on goal, you can’t score.
“And we can’t blame the ball, because it flew fairly well, as you could see with the goal Tevez scored.
“Overall we were a bit too hesitant and that continued throughout the game.
“We were always chasing the ball behind and we deserved to be kicked out.”
Having reached the Champions League’s knock-out stages for the last three years, tenth-placed Dortmund face an uphill task to qualify for next year’s tournament as they need a top four finish in Germany’s top flight.
“It will be a pity if that is our last Champions League match for a year and a half,” admitted Dortmund captain Mats Hummels.
“We have had some wonderful evenings, but this year we have simply not had the condition to do well in the Champions League.”