Returning to the Champions League after two decades, Newcastle travelled to Dortmund needing a win to put them back on course for a place in the last 16, but they were outclassed by the German side from start to finish.
Niclas Fuellkrug struck midway through the first half before Brandt wrapped up the game on 79 minutes.
The victory saw Dortmund provisionally go top of a difficult Group F with two games remaining, three points clear of Newcastle and with the head-to-head advantage.
"When you concede four goals in this stadium three days ago, it feels good to hold a very good English team to nil -- and the two goals will do us good," Brandt told Amazon Prime as Dortmund bounced back from Saturday's 4-0 thrashing by Bayern Munich.
Paris Saint-Germain can regain their lead in the section by avoiding defeat at AC Milan later on Tuesday.
"We weren't at our best tonight. Our intensity, our quality was missing, but that said we still had our moments," said Newcastle manage Eddie Howe.
The Magpies realistically need to win their remaining games away to PSG and at home to Milan if they are to advance.
Dortmund coach Edin Terzic toasted his side's "really good performance as a complete team".
"We let very little get by us and we had the game in our grasp," he told Amazon Prime.
Injury-hit Newcastle travelled to Dortmund without a full complement of players, Howe losing defenders Dan Burn and Matt Targett to long-term injuries in his side's 1-0 win over Arsenal on the weekend.
Comprehensively outplayed just three days ago by a Harry Kane-powered Bayern, Dortmund began confidently as Fuellkrug and Karim Adeyemi unleashed fierce shots on Newcastle's goal within the opening 15 minutes.
The 30-year-old Fuellkrug, 12 months on from making his Germany debut, broke the deadlock midway through the half, scoring his first goal in the Champions League, prodding in a cross from Marcel Sabitzer.
Felix Nmecha, who scored the game's only goal at St James' Park last month, along with Brandt controlled play in midfield, always seemingly at arm's length from the undermanned Newcastle defence.
The sides traded blows early in the second, Dortmund's Brandt forcing saves from Nick Pope either side of Joelinton powering a header wide for Newcastle.
A tired Adeyemi gave away a dangerous free-kick to the left of the box with 10 minutes to go, but Kieran Trippier's delivery was easily cleared and Dortmund hit their opponents on the counter to kill off the match.
Adeyemi won the ball back and blasted a perfect pass into Newcastle's half, into the path of the onrushing Brandt.
The Dortmund midfielder made the most of the two-on-one, shaping to pass before steering past a helpless Pope to double the lead.
Dortmund's win means they are the only side to have beaten Newcastle in the Premier League side's past 13 matches, having now done so twice in a fortnight.
