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
Hazard smashed the ball past Rui Patricio in the 92nd minute after constant pressure from the home side, who are bidding for a top-four place.
Patricio made a sharp save shortly afterwards from striker Gonzalo Higuain and another from Willian in the dying minutes. Chelsea had 22 shots to the visitors' two and also enjoyed 76 percent of possession.
The result leaves Chelsea in sixth, level with Arsenal and behind Manchester United who were playing each other later on Sunday.