The close-season signing from Shaktar Donetsk opened the scoring, but Vaclav Kadlec hit back with his first Frankfurt goal in the 35th minute.
Mkhitaryan added another after the break though, to send Dortmund to the top of the Bundesliga as they maintained their 100 per cent record.
Dortmund made one change from their 1-0 win over Werder Bremen last week, with Sven Bender replacing Sebastian Kehl in midfield.
For the hosts, recent signings Stephan Schrock and Kadlec both featured in the starting line-up as Armin Veh's men went in search of consecutive Bundesliga wins.
Frankfurt started brightly and created an early chance when Japan international Takashi Inui tested Dortmund goalkeeper Roman Weidenfeller.
At the other end, Marco Reus set up Jakub Blaszczykowski, but he could only fire straight at Frankfurt goalkeeper Kevin Trapp.
Dortmund did score an early goal though, as Armenian Mkhitaryan calmly slid home a through ball.
Blaszczykowski slipped the ball in behind the Frankfurt defence and Mkhitaryan did the rest, timing his run well before slotting a left-footed effort past Trapp.
Kadlec had a terrific chance to level proceedings but was denied by good defending from Marcel Schmelzer, before Weidenfeller kept out the dangerous Czech forward moments later.
Kadlec was a constant threat though, and opened his Frankfurt account 10 minutes before the break after reacting quickly to a loose ball.
Stefan Aigner headed a deep Inui cross from the left against the post, and Kadlec was on hand to score the rebound to send the two sides in to the break at 1-1.
Mkhitaryan fired Dortmund ahead with his second goal of the match 10 minutes into the second half with an excellent finish.
The attacking midfielder cut in from the right before dribbling along the edge of the penalty area and striking powerfully past Trapp.
Dortmund almost scored a third goal shortly after, but defender Neven Subotic saw his header hit the post.
The visitors enjoyed good spells of possession in the latter stages but could not find another goal to kill the game off.
They held on for victory though, as Jurgen Klopp's men – who have lost just two Bundesliga matches on the road since September 2011 - made it four wins from as many matches this season.
