Kimmich: I have never experienced anything like this season
Niko Kovac's side moved up to second place with a 3-0 victory over their Bavarian rivals Nurnberg, but they remain nine points behind leaders Borussia Dortmund, who beat Schalke 2-1.
Kimmich's corner set up Robert Lewandowski's opener, with the Poland striker adding a second before the half-hour – Franck Ribery's first league goal of the season adding further gloss late on.
And the youngster, who went agonisingly close to adding a fourth in stoppage time with a long-range strike that rattled the crossbar, is relishing the task of catching up with Dortmund.
"I have never experienced anything like this season," Kimmich told Bayern's official website.
"Last season we were a bit behind, but this season the gap is bigger.
"Dortmund have won again. That's why the season is really exciting.
"Now we have another situation and this can show if we also have guys in the team to play in this situation."
42 - Robert Lewandowski scores his 42nd brace in the #Bundesliga, only Gerd #Müller has scored more (55). Force. #FCBFCN— OptaFranz (@OptaFranz) December 8, 2018
Kovac named an unchanged side for Saturday's encounter at Allianz Arena, and the Bayern boss' faith was justified by a dominant display.
"We have allowed almost nothing for over 90 minutes," Kovac told Bayern's official website.
"We ourselves had many possibilities. I am satisfied with the performance. It was important that we did not lose the lead.
"Positive results are always important. We have now won three games in a row, I am satisfied."
Kovac's focus will now switch to the Champions League clash with Ajax on Wednesday, with top spot in Group E at stake.