Bayern's clash with Bundesliga title rival Borussia Dortmund is coming up next Sunday (AEDT), with the great rivals sitting first and second in the Bundesliga.
Dortmund briefly occupied top spot this Sunday (AEDT) after a 3-1 win over Wolfsburg, a match in which Erling Haaland returned from injury with a goal.
But it was nudged off the summit later in the day when Leroy Sane's 71st-minute strike earned a depleted Bayern three valuable points.
Eight days previously, Bayern was beaten by Augsburg, so a league win of any sort this time was to be welcomed.
Nagelsmann's squad has been hit hard by COVID-19 cases, but the head coach saw enough from the team he fielded against Arminia to be optimistic about the tussle with Dortmund.
The Bayern boss said: "I am very satisfied. It was a step forward after the Augsburg game.
"We had enough chances to win the game. We gave away a few chances in the second half. Dortmund won, so we were under a bit of pressure. It's a deserved victory. We don't always have to score three, four or five goals. One is enough.
"Overall, we defended well. Such games are important. If you lose those games, then it's not enough to just win games like next week.
"We are now heading to Dortmund as championship leaders and full of anticipation."
Sane's goal was Bayern's 102nd in the league this calendar year – a Bundesliga record, beating Cologne's mark from 1977.
Thomas Muller made his 396th Bundesliga appearance for Bayern, matching the great Franz Beckenbauer's total and going sixth on the club's all-time list, led by Sepp Maier (473).
Asked how many more games he could play, midfielder Muller said: "We'll see. If I stay fresh and fit, and well enough, then something is still possible. That is just a nice statistic, it simply shows the path I have already taken.
"But I am looking forward more to the road still ahead of me, which is certainly a bit shorter in comparison."