Dortmund had to wait until the 34th minute for another chance to arrive, but they took full advantage on this occasion as Adrian Ramos collected a clever pass from Grosskreutz before drilling the ball past Burki.
Grosskreutz's runs forward were proving to be a problem for the visitors, and he was inches away from scoring Dortmund's second when he dragged an effort just wide of the post.
Freiburg's attempts to remain just one goal behind before the break ended in failure as Kagawa, making his second debut for Dortmund after moving back to the club from Manchester United, slotted home after linking up with Ramos.
The hosts quickly took control of the match once again, but Henrikh Mkhitaryan was guilty of being wasteful in front of goal as he sent a great chance over the crossbar.
Another substitute, Pierre-Emerick Aubameyang, wrapped up the win with 12 minutes remaining by catching Burki off balance with a fine strike from inside a congested area.
However, there would be a late consolation for Freiburg when Oliver Sorg broke free of the Dortmund defence to stroke the ball past Wiedenfeller.