The Dortmund captain struck in style just before the hour mark to move Jurgen Klopp's side four points clear of third-placed Bayer Leverkusen, who could only draw at Hannover on Saturday.
Kehl instinctively shot after Kevin Grosskreutz fed the ball into his path, with the 25-yard effort curling over Freiburg goalkeeper Oliver Baumann and into the back of the net.
The midfielder's first goal in any competition since April 2012 secured the three points for Dortmund, but they were made to work hard by the relegation-threatened hosts.
Christian Streich's side felt Dortmund defender Sokratis Papastathopoulos should have been sent off for bringing down the impressive Philipp Zulechner on the stroke of half-time.
And Freiburg were made to rue their luck, too, as they remained in the bottom two of the Bundesliga.
Hampered by the absence of Robert Lewandowski (knee) and Marco Reus (foot), Dortmund started slowly, with a weak Nuri Sahin free-kick all they could muster in the early stages.
Pierre-Emerick Aubameyang fired wide after a neat team move but Freiburg were well organised at the back, frustrating their opponents, who had won the last seven meetings between the two sides.
Zulechner, making his first Freiburg start since arriving from Austrian side Grodig last month, shot over after a corner was not properly cleared, but the home fans were the liveliest aspect of a tame first 30 minutes.
Mats Hummels' well-weighted long ball could have caused Freiburg problems but Baumann was quick to react before the first half's major talking point angered the hosts.
Zulechner, who was sent through on goal, was hauled down by Sokratis in the 43rd minute, but the Greece defender – who was the last man – was only given a yellow card.
Dortmund capitalised on their good fortune with a promising start to the second half as Julian Schieber, deputising for top scorer Lewandowski up front, shot into the side netting.
Schieber then agonisingly missed a teasing ball across the face of goal from Henrikh Mkhitaryan in the 54th minute but the visitors soon had the lead, with Kehl's piece of brilliance leaving Baumann with no chance.
Freiburg battled for an equaliser and regularly got into good positions, with Ahmed Mehmedi a constant threat.
Dortmund nearly scored again, with substitute Jonas Hofmann blazing over from close range after Aubameyang's cut-back in the dying stages, but one goal was enough as Klopp's charges continued their excellent record against Freiburg.
