Hannover remained compact, however, forcing the home side to be patient in the face of its defensive setup.
"We know that we can play better. We'll happily take the three points, though," Dortmund coach Thomas Tuchel said.
Ilkay Gundogan fired over after the break before Mkhitaryan finally scored in the 57th.
A Hannover attack broke down and the ball fell to Gundogan. He found Reus, who passed to Mkhitaryan. Marcel Schmelzer provided a dummy run on the left and Mkhitaryan, faced by a host of defenders backing off, saw his chance and let fly inside the right post.
"I got the ball from Marco Reus. I wanted to play a one-two but then I saw there was a man behind. So I moved inside and wanted to shoot in the far post, and I did it," Mkhitaryan said. The Armenian has 18 goals and 17 assists across 33 competitive games this season.
Hannover slumped to its seventh straight defeat and was seven points from safety.
"We weren't rewarded, as is often the case, but we'll keep going and get our reward," Hannover coach Thomas Schaaf said.
League top-scorer Pierre-Emerick Aubameyang sat out the game for Dortmund due to a foot injury.
Bayern can restore its eight-point lead with a win at Augsburg on Sunday.
Hoffenheim drew 1-1 at Werder Bremen in Julian Nagelsmann's first game in charge of the visitors. The 28-year-old Nagelsmann is the youngest coach ever in the Bundesliga and got off to a great start when Andrej Kramaric put his side ahead in the 10th minute.
However, Papy Djilobodji equalized three minutes later and Hoffenheim was left hanging on after Kramaric was sent off with a second yellow card in the 77th.
"From that point of view we can talk about a point won," Nagelsmann said.
Elsewhere, Stuttgart upset Hertha Berlin 2-0, Bayer Leverkusen took advantage of Hertha's slip and defeated Darmstadt 2-1 to move third, while Wolfsburg beat Ingolstadt 2-0 to end its seven-game run without a win.
Host Cologne defeated Eintracht Frankfurt 3-1 in the late game to leave the visiting side one point off the relegation zone.
Dominique Heintz put Cologne ahead with a header from a free kick in the 57th, before Gerhardt returned the earlier favor for Modeste to wrap up the win in the 72nd.
In Stuttgart, Serey Die's first Bundesliga goal put the home side ahead in the 51st. American defender John Anthony Brooks hit the post for Hertha five minutes later but Filip Kostic sealed Stuttgart's fifth straight win in the 84th.
"It doesn't have to end, it can keep going," said Stuttgart coach Juergen Kramny, whose side climbed 10th after being bottom in mid-December.
In Wolfsburg, Daniel Caligiuri crossed with the outside of his boot for the in-rushing Julian Draxler to convert past Ingolstadt keeper Ramazan Ozcan in the 29th and Robin Knoche made it 2-0 10 minutes later.