Having seen their hopes of defending their DFB-Pokal trophy dashed by Bayern Munich, and with a practically impossible task of chasing down the same opponents to defend their Bundesliga title, failure to progress beyond the Ukrainians would end all realistic hopes of a trophy.
Germany's double winners prepare to face Shakhtar on Tuesday night having drawn 2-2 in Ukraine last month, and they are keen to complete the job in front of their own fans.
"We don't want to see the next round of Champions League games from our own sofas," Dortmund director of sport Michael Zorc told Kicker magazine.
"We have the keys (to the next round) in our own hands."
The score draw away from home tipped the scales only slightly in Dortmund's favour, and now is the time for them to prove Manchester United manager Sir Alex Ferguson right when he mentioned them as one of the favourites for the title.
"The tie is poised well for us, and we are playing at home," full-back Marcel Schmelzer told www.dfb.de.
"If we concentrate like we have been doing recently, then we will go through. But if we give just a little, then it will be tough against Donetsk."
Dortmund discovered that much in the first leg, when a late goal from Mats Hummels saved them from defeat and ensured they remain one of only three clubs still unbeaten in the current competition.
Yet Shakhtar's away form has been impressive with Juventus only managing a 1-1 draw against them in Turin, while Mircea Lucescu's side have only failed to score once in their last 11 away fixtures in the Champions League.
"They are particularly dangerous up front," Schmelzer said. "We are going to have to pay good attention to their quick Brazilian.
"They are also still very fresh. After facing us nearly three weeks ago, they have only had one game in the Ukrainian league after the winter break."
That 91-day winter break ended last weekend with Shakhtar carrying on from where they left off in 2012 with a 4-1 win over Volyn Lutsk, a result which gave them a 13-point advantage at the top of the Ukrainian league and enables them to concentrate all of their efforts on Tuesday night's game.
"We are going there to attack," added Lucescu, whose side scored eight of their 12 group stage goals away from home.
Dortmund would prefer to have their first-choice defence available, but Hummels is still a doubt after missing their last two games due to a bout of flu.
"I think it's not only myself but the whole team who miss him," said Schmelzer. "It's a different game when Mats is not there.
"Nevertheless, I think Felipe (Santana) is settling in better minute by minute and we're pleased to have three strong central defenders."