Two first half strikes from the BVB were enough to condemn the Serie A side to defeat at Signal Iduna Park ahead of next week's second leg encounter in Italy.
Germany's attacking midfielder Brandt, who captained Dortmund against the Italian side, expressed satisfaction with the result in Dortmund and is confident they can secure progression into the Round of 16.
"Overall, we're satisfied with the game," said Brandt in the mixed zone after the match.
"I would have liked us to have scored another goal in the second half. I think we had one or two more chances that we could have taken. A 2-0 lead is a bit tricky.
"But it also gives you a bit of security because you've kept a clean sheet and scored two goals. Overall, we're satisfied and will head to Bergamo full of confidence next week."
The German side will be looking to progress past the play off stage of the tournament for the second consecutive season.
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Galatasaray produced a stunning second-half surge to seize control of their UEFA Champions League knockout phase play-off, hammering Juventus 5-2 in a chaotic first-leg encounter in Istanbul.
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Borussia Dortmund secured a commanding 2-0 victory over Atalanta in the first leg of their UEFA Champions League knockout phase play-off, taking a valuable advantage into the return fixture in Italy.
