Mkhitaryan leads Dortmund to win
Mkhitaryan, a 27.5-million euro ($35.4 million) offseason signing from Shakhtar Donetsk, opened his account for his new side in the 10th minute, when Jakub Blaszczykowski timed his pass perfectly to set the Armenian up.
Another offseason signing, Frankfurt's Czech striker Vaclav Kadlec, equalized in the 36th, converting the rebound after Stefan Aigner's initial headed effort crashed back off the crossbar after a great cross from Takashi Inui.
Mkhitaryan produced a fine individual effort for what proved to be the winner in the 56th, collecting the ball from Kevin Grosskreutz near the touchline, advancing past a defender and then unleashing a shot with his left boot inside the far post.
''I feel very good in Dortmund and am very happy to have scored my first goal,'' Mkhitaryan said. ''Of course it's even nicer that I scored a second one too.''
Frankfurt was left to rue missed chances, with Dortmund doing just enough to grind out the hard-fought win.
''I think we deserved a draw. We had chances in the first half, like they did. We were at the same level in the second half,'' said Frankfurt coach Armin Veh.
Nevertheless, Dortmund coach Juergen Klopp was relieved to get the three points.
''We have to play better football, there's no question,'' Klopp said. ''I've seen a few weaknesses in our build-up play and ideally we need to defend better. Still, with 12 points after four games, this is complaining at a high level.''
''The lads put the plan into action very well,'' said Schneider, who took over on Monday after Bruno Labbadia was sacked for starting the league with three straight defeats. ''There were a lot of elements in place which made it so much fun.''
Alexandru Maxim set up Antonio Ruediger's opening score in the 12th minute and delivered a corner for Ibisevic to score with a header seven minutes later.
Kevin Volland pulled one back with a deflected shot in the 26th, but Maxim capitalized on a missed clearance from Hoffenheim keeper Koen Casteels to score two minutes later.
Ibisevic scored his second two minutes after the break, when he shrugged David Abraham off the ball, rounded Casteels and slotted to the empty net.
Maxim capped a fine performance with a wonderful strike inside the far corner in the 55th, before Ibisevic completed his hat trick with another header in the 63rd.
Roberto Firmino claimed an 87th-minute consolation for Hoffenheim.
''It was an off-day for us,'' Hoffenheim coach Markus Gisdol said.