Kehl, a former Freiburg midfielder, returned to haunt his former club with a stunning 25-yard strike that settled Sunday's fixture at the Mage Solar Stadion.
Dortmund's hard-fought 1-0 win saw them move four points clear of third-placed Bayer Leverkusen and, although runaway leaders Bayern Munich are almost beyond catching, finishing as runners-up would represent a good result for Jurgen Klopp's side this season.
They have battled an injury crisis and the departure of Mario Gotze to Bayern Munich, while they were hit by the news that star striker Robert Lewandowski will also join the European champions at the season's end.
Captain Kehl's second-half goal was an instinctive strike from distance, with his effort curling over Freiburg's Baumann, who was off his line, and into the back of the net.
"I knew that Oliver Baumann stands quite far off his line," Kehl said.
"I always like coming back to Freiburg. (They) did a great job.
"They didn't let us play and we didn't create much at all. It was a tough game."
Dortmund coach Klopp admitted that his side were not at their best but bemoaned wasted chances in front of goal.
"(It was) a tough match. Freiburg has (been) able to create chances," Klopp said.
"We have made a lucky goal. We have not done that (take our chances), (and) as a result, we had to work up to the last moment."
