Robert Lewandowski's long goal-scoring streak ended at 15 consecutive Bundesliga games – one short of Gerd Muller's record – but the champion moved three points clear of Wolfsburg regardless.
That is now 40 goals in its past eight matches for ruthless Bayern, which led 2-0 courtesy of great finishes from Thomas Muller and Kimmich at half-time.
Bayern has won eight consecutive matches in a great start to Julian Nagelsmann's reign and midfielder Kimmich says there is more to come.
The Germany international said: "The character of the team is great. We have players who want to develop, who are hungry.
"We want to win every game. We're in good form at the moment, but we haven't been able to manage all of the games this season with confidence. There's room for improvement."
Kimmich, who delivered the free-kick that was turned into his own net by Griesbeck, added: "It wasn't exactly a brilliant performance on our part, but we had the game under control even when we played with 10.
"We made mistakes in the first half, and we kept inviting Furth via set-pieces."