Felix Nmecha scored the only goal as the woodwork twice denied Newcastle an equaliser in the closing stages.
The German giants' first win in what is widely regarded the toughest group in the draw lifts Dortmund above Newcastle on head-to-head record with both sides on four points.
Paris Saint-Germain lead the section on six points with last season's semi-finalists AC Milan bottom on two.
Newcastle had announced their return to the Champions League stage for the first time in 20 years in style with a 4-1 demolition of PSG three weeks ago.
But the Magpies were handed a deserved reality check after a surprisingly flat performance.
"Tactically they were good and gave us problems in central areas. In the second half we were a lot better and unfortunately the ball would not go in," Howe told TNT Sports.
"The woodwork denied us but we have to look at ourselves, own the defeat and do it the hard way in the group."
Dortmund had failed to score in their opening two games in the group, but their defeat by PSG last month was the only time they have lost in 12 matches so far this season.
The visitors dominated the opening 45 minutes, but should still have fallen behind when Anthony Gordon fired straight at Gregor Kobel with just the Swiss goalkeeper to beat.
Newcastle were then dealt a major blow when former Dortmund striker Alexander Isak was forced off with injury.
Donyell Malen and Niclas Fullkrug tested Nick Pope but it was an inspired piece of play from a centre-back that eventually helped Edin Terzic's men break their duck.
Nico Schlotterbeck robbed Gordon of possession in midfield and burst forward before crossing for Nmecha to stroke into the far corner in first-half stoppage time.
"Perfect result for us," said Terzic. "We played a fantastic first half and showed fantastic fight second half.
"In the second half we had to defend a lot but we did it with a lot of passion, a bit of luck and a great goalie."
