Kehl's match-winner just before the hour came during an improved second-half performance from Dortmund, who were not at the races in the first 45 minutes.
Jurgen Klopp's men had chances to add a second late on as Freiburg ran out of steam, losing for the sixth time at home this season and remaining second from the bottom of the Bundesliga after missing the chance to move out of the relegation zone.
Freiburg started the better with the lively Philipp Zulechner making an impressive first start for the club.
Dortmund, without the injured Robert Lewandowski, rarely threatened and only one dangerous ball into the area had Freiburg goalkeeper Oliver Baumann sweating, but Pierre-Emerick Aubameyang and Lukasz Piszczek both failed to get on the end of it.
Sokratis Papastathopoulos was lucky not to give away a penalty as he blocked a shot with his hand, but he saw a yellow card soon after for a foul on Zulechner as he approached the penalty area at full speed.
For all their possession, Freiburg were unable to pose a serious threat to Roman Weidenfeller's goal with Jonathan Schmid's curling free-kick missing the target at the conclusion of the first half.
Dortmund were much improved in the second half and they took the lead when Kevin Grosskreutz brought the ball in from the left and let Kehl curl in a first-time shot which dipped over Baumann.
He raised one hand, half in celebration and half apologetically, aware of what that goal could mean to Freiburg.
The hosts tried to respond, but they lost their defensive organisation and Aubameyang nearly capitalised when he was put through on goal.
He chose to pass the ball and Jonas Hofmann blazed his shot over the goal, which was guarded by three Freiburg defenders.
Hofmann had another shot on Baumann's goal before Grosskreutz sent in the last shot of the game with Freiburg already beaten.