The German champions won 3-0 on the night for a 5-2 aggregate success with two first-half goals that killed off the tie and another on the hour to cap a fine performance as they reached the last eight for the first time in 15 years.
Central defender Felipe Santana, a replacement for Mats Hummels, headed home on the half hour and Mario Gotze added another in the 37th for Dortmund who have come a long way since they were on the brink of bankruptcy in 2005.
Poland international Jakub Blaszczykowski's close-range effort then buried any lingering hopes for Shakhtar who had come out fighting in the second half but never looked likely to break Dortmund's unbeaten run in the Champions League this season.
After two trophy-laden seasons Dortmund trail Bayern by 17 points in second place in the Bundesliga and were also dumped out of the German Cup by their chief rivals last week.
However, they have won every home game in the Champions League this season after also beating Real Madrid, Ajax Amsterdam and Manchester City in the group stage.
"This is an extraordinary moment for us," Dortmund coach Jurgen Klopp told reporters. "The whole Champions League season has been going so well for us. For 80 minutes we offered a superb game apart from a short spell after the break."
"It was a strong performance. We played good football but remained focused," he said.
Shakhtar coach Mircea Lucescu acknowledged Dortmund's superiority.
"Overall, the result corresponds with what we saw on the pitch. I believe Dortmund deserved to go through," said the Romanian. "I hope they reach the final as they are a really strong side."
LEWANDOWSKI CHANCE
Dortmund's recent domestic setbacks and swirling speculation over forward Robert Lewandowski's potential transfer to Bayern did little to dampen their attacking play.
Lewandowski almost put them in front when Goetze sent him through with a defence-splitting pass but the Pole's shot was blocked by keeper Andriy Pyatov.
Former European champions Dortmund, driven on by an impressive 65,000 crowd, kept up the pressure but their finishing was less than clinical.
There was nothing complicated about Santana's header in the 31st minute though, the Brazilian rising high above marker Yaroslav Rakitskiy to nod in a Gotze corner at the near post.
Santana was again replacing central defender Mats Hummels, who scored a late equaliser to secure a 2-2 draw in the first leg in Ukraine but is out of action with flu.
With Shakhtar now on the back foot, 20-year-old Gotze, in sparkling form, turned scorer six minutes later with a sweeping finish after a well-timed Lewandowski cutback that left Shakhtar's defenders again exposed.
The Ukrainians, who are just back from a three-month winter break, almost pulled one back after the restart with substitute Douglas Costa firing narrowly wide as they poured forward in search of a quick goal.
Pyatov, though, spilled a tame shot from Ilkay Gundogan into the path of Blaszczykowski in the 59th minute allowing the midfielder to s
