Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
City, who made nine changes for the game, could still secure the title this weekend if second-placed Manchester United lose at Aston Villa on Sunday.
Raheem Sterling put City ahead in the 44th minute and within two minutes they had a chance to double the lead from the penalty spot, but Sergio Aguero's soft chip down the middle was easily saved by Edouard Mendy.
Chelsea drew level through a low drive from Hakim Ziyech in the 63rd minute, and went on to grab a late winner through Marcos Alonso.