In an evenly balanced game in which Freiburg refused to concede any space without a battle, Dortmund struggled to create scoring chances with just three shots on goal - all from outside the box - in the first half.
With top striker Robert Lewandowski and Marco Reus on their growing injury list, Dortmund, who take on Zenit St Petersburg in the second leg of their Champions League round of 16 tie later this month, needed almost an hour to break the deadlock.
Experienced former Germany international Kehl did not hesitate to float an audacious 25-metre shot over keeper Oliver Baumann in the 58th minute for his first goal since April 2012.
"Oliver Baumann is known for venturing out of his goal and I had seen that during the game," Kehl told reporters. "But the goal needed a bit of luck as well."
The result moved Dortmund to 48 points, four ahead of third-placed Bayer Leverkusen, who drew 1-1 at Hanover 96 on Saturday and Schalke 04, 4-0 winners over Hoffenheim.
"That was a very hard game," Dortmund coach Juergen Klopp told reporters.
"Freiburg, despite dominating, did not create chances and then we scored a lucky goal. We failed to add another and we had to work until the very end.
"Whoever wins such games normally wins the championship but that is not possible any more," he said leaders Bayern's 20-point gap.
Coach Christian Streich of Freiburg, who have gone six matches without a win and are in 17th place on 19 points after their eighth loss in a row to Dortmund, was fuming at the referee for not sending one Dortmund player off in the 43rd.
"Every two weeks we seem to be the idiots," Streich said. "I really am in no mood to watch this because it is catastrophic the way we are beaten down by certain gentlemen."
Streich said referee Peter Gagelmann should have sent off Sokratis Papastathopoulos for a foul on Philipp Zulechner as the last man.
"That should have been a red card," he said. "There is a rule for that."
In the other game on Sunday, Hertha Berlin and Mainz 05 drew 1-1, losing ground in the battle for the European spots.
Bayern Munich continued their march towards the title with a 6-1 demolition of VfL Wolfsburg for a league record 16th successive win on Saturday and stayed 20 points clear at the top.
- Sports & Recreation
- Robert Lewandowski
- Oliver Baumann
- Zenit St Petersburg
- Marco Reus