Marco Reus twice canceled out goals from Robert Lewandowski at Signal Iduna Park on Saturday before Paco Alcacer came off the bench to score a dramatic winner for Favre's men, racing on to Axel Witsel's pass to beat Manuel Neuer with a brilliant dinked finish, FourFourTwo reported.
While Dortmund is still only four points clear at the top – with Borussia Monchengladbach second – it pushed seven ahead of Bayern.
But Favre refused to rule out Bayern and said the Bundesliga title race was still well and truly alive.
"We're on top of the table in the Bundesliga and Gladbach is second," he told a news conference.
"Who is number three again? Bayern. It's very close.
"There is [RB] Leipzig, Gladbach and of course Bayern Munich, [especially] when it plays like they did [against Dortmund]."
Favre hailed Dortmund's comeback but accepted his side was fortunate at times, with Bayern having been on top throughout the first half, while Lewandowski saw a stoppage-time equalizer rightly ruled out for offside.
"It was a crazy game. Bayern were very strong in the beginning," Favre said. "They clearly dominated us, had plenty of possession and we could not keep the ball. If we got it, we lost it again.
"That was very hard. But I knew they could not keep up the pace. The pace was very high. 'Gegenpressing', pressing, ball-winning, everything was perfect.
"We could not hold any balls. It was like a boomerang. We had to wait, we waited and luckily it was only 1-0 at half-time.
"After Reus' [second] goal the crowd was there, and we felt we could win, and we did it. The morale was fantastic."
Niko Kovac was satisfied with Bayern Munich's performance against Bundesliga leader.
"We saw a fantastic football match from both sides today. It was an open game," Kovac said in quotes reported on the Bayern website.
"In the first half we had the game in hand, in the second half Dortmund [did].
"After 1-1 we managed to come back again. Then we conceded twice; that must not happen to us. We closed the midfield very well in the first half and drove the opponent out. In the second, we did not succeed, there were then the chances.
"Unfortunately, we lost the game, even though it could have been a draw. You can be satisfied with the performance. That was the best game since Schalke: playful, combative and tactical, especially in the first half. We will have to build on that and deliver more games in the future."