Wednesday's 2-2 draw with Shakhtar Donetsk in Ukraine gives the Bundesliga side a small advantage in terms of away goals, meaning a 0-0 or 1-1 draw in the second leg at the Westfalenstadion would be enough to take them beyond the last-16 tie, and captain Sebastian Kehl is optimistic.
"We can live with a 2-2," Kehl said after Wednesday night's match. "Two goals away from home mean that we can now finish them off at home."
Kehl celebrated his 33rd birthday with just the present he was hoping for.
"I wanted a good game and a decent result, and we got both of them," he said on his club's website.
"We didn't concede much and we were always dangerous in attack. The important thing was learning from the weekend and it is a quality of this side that we are always able to bounce back."
Coach Jurgen Klopp was "totally satisfied" with the outcome, praising his side's temperament after falling behind twice.
Darijo Srna put the Ukrainians ahead with a sweetly-struck 31st-minute free-kick before the prolific Robert Lewandowski levelled 10 minutes later.
Substitute Douglas Costa restored the home team's advantage in the 68th minute before Mats Hummels handed the Bundesliga outfit a second away goal with a header three minutes from the end.
"It's a real cauldron here and we were very strong," Klopp said. "We were punished twice for losing concentration, but the team fought back twice and played great football for long spells.
"We were dangerous without creating any real chances, but we had enough of them to score more goals than we did. Everything's fine with 2-2."
Dortmund host the Ukrainian champions on March 5 as they bid to reach the last eight for the first time since 1998, the year they were beaten semi-finalists as they tried to defend their title.