At the other end of the table, Julian Nagelsmann, at 28 the Bundesliga's youngest-ever coach, made his debut on the Hoffenheim bench and watched his side draw 1-1 at Werder Bremen in a crunch relegation battle.
Dortmund, missing league top-scorer Pierre-Emerick Aubameyang through injury, struggled to break down Hanover in a match which pitted the Bundesliga's best attack against its second-worst defence.
The finally broke through in 56th minute when Mkhitaryan collected the ball just inside the Hanover half, ran at the defence, cut inside and unleashed a 25-metre shot which flew past Ron-Robert Zieler.
Dortmund, five points behind Bayern who face Augsburg on Sunday, have scored 53 goals this season and the game could have been much easier if Marco Reus had converted one of two early chances.
Reus, almost back to his best after injuries and illness, was denied when Zieler somehow kept out his effort from point-blank range and again when his free kick smacked against the crossbar.
Hanover, who have conceded 36 goals, held firm until Mkhitaryan struck his eighth goal of the season.
Hoffenheim, one off the bottom of the 18-team table, were facing Werder Bremen, who are one place and five points ahead of them in the relegation playoff spot.
Kramaric gave Nagelsmann a dream start when he headed in after 10 minutes, but Bremen levelled three minutes later when defender Papy Djilobodji scored with a deflected effort following a corner.
Kramaric was sent off with 13 minutes left for a second bookable offence but Hoffenheim held on.
Bayer Leverkusen moved into distant third, 13 points behind Dortmund, by coming from behind to win 2-1 on a difficult pitch at Darmstadt.
A blunder by Leverkusen goalkeeper Leno, who failed to hold the ball following a throw-in, allowed Wagner to head Darmstadt in front after half an hour.
But another moment of misfortune, this time by Darmstadt defender Aytac Sulu who headed into his own goal, allowed Leverkusen to level just after the hour before Julian Brandt snatched the winner in the 77th minute.
Hertha Berlin dropped to fourth, behind Leverkusen on goal difference, after losing 2-0 at VfB Stuttgart, who notched their fifth win in a row.
Ivorian midfielder Serey Die opened the scoring with a superb strike with the outside of his foot just after halftime and Filip Kostic added the second.
Julian Draxler and Robin Knoche scored as VfL Wolfsburg overcame Ingolstadt 2-0 to claim their first win of 2016.
(Writing by Brian Homewood, editing by Ed Osmond)
Share
