The much-fancied German champions put in a dominant display on home soil to prevail 5-2 on aggregate.
Mario Gotze provided the moments of inspiration for Dortmund in the first half, with the talented playmaker sending over the corner from which Felipe Santana broke the deadlock and adding the second himself as he steered home a cross from Robert Lewandowski.
Jakub Blaszczykowski added a third shortly before the hour mark, with Shakhtar goalkeeper Andriy Pyatov spilling a shot into his path and allowing the ball to be walked into the net.
Dortmund started very much on the front foot and nearly took the lead with their first real sight at goal. Lewandowski latched on to Gotze's pass to go clean through but the Pole was thwarted by Pyatov's legs.
Sven Bender's drive from distance sailed harmlessly over before Shakhtar started to grow into the game and reminded Dortmund of their attacking prowess when Alex Teixeira's teasing free-kick into the area produced a hesitant clearance from Marcel Schmelzer.
While fellow Brazilian Fernandinho poked wide from the edge of the area, the visitors fell behind in the 31st minute. Santana leapt above his marker to head home Gotze's corner at the near post, with Shakhtar defender Razvan Rat failing to clear despite being positioned on the line.
Jurgen Klopp's men continued to pour forward and were duly rewarded with their second of the evening six minutes later. Lewandowski burst down the right and his low cross was tickled goalwards by Gotze, with the ball taking a deflection off a Shakhtar defender before nestling into the net.
Shakhtar came out all guns blazing after the interval, with Luiz Adriano firing across Roman Weidenfeller and inches wide of the target.
They were leaving themselves open at the other end, although the 1996-97 European champions were grateful for a sloppy piece of keeping from Pyatov to go further ahead.
Ilkay Gundogan's strike from the edge of the area was straight at Pyatov but he spilled the ball, allowing Blaszczykowski to steal in, skip past the keeper and tap in from close range in the 59th minute.
Not content to rest on their laurels, Dortmund continued to push forward, with Marco Reus bursting through on goal but he found himself off-balance and his strike missed the target.Mircea Lucescu's side had an opportunity to end a forgettable evening on a high, with a deflected shot falling into the path of Adriano, who was denied by the legs of the onrushing Weidenfeller.
|Borussia Dortmund||Team Statistics||Shakhtar Donetsk|
|2||1st Half Goals||0|
|8||Shots on Target||4|
|5||Shots off Target||4|
|63.4||1st Half Poss.||36.6|
|44.3||2nd Half Poss.||55.7|