Niclas Fullkrug opened the scoring for the hosts midway through the first half, with Julian Brandt adding a second from a superb counter attack late on as the Germans completed a Group F double over their English opponents.
Newcastle's best chance fell to Joelinton just after the break but the midfielder headed Tino Livramento's cross wide from five yards out.
The Brazil international's effort was a rare clear sight at goal for Newcastle, with Edin Terzic's Dortmund side having controlled much of the first period.
They enjoyed the better opportunities despite a much-improved second-half display from the injury-hit visitors.
Newcastle's return to Europe's elite competition began in fine fashion with a draw at AC Milan before they thrashed Paris St-Germain on Tyneside.
However, they now face an uphill challenge to progress further, with Dortmund's victory at St James' Park and again in Germany on Tuesday, moving them three points clear of Newcastle, who travel to PSG in their penultimate group match.
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