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
The Spaniard suffered his biggest-ever defeat in league football after they had enjoyed the lion's share of possession and chances but paid for sloppy defending that led to the Belgian powerhouse Lukaku converting his 12th league goal of the season after 34 minutes.
Kevin Mirallas struck right after the break and excellent 18-year-old academy graduate Davies dinked a brilliant first goal for his boyhood club as City looked increasingly clueless.
Coming hot on the heels of their last loss in Merseyside at Liverpool on New Year's Eve, City were left in fifth place, now 10 points adrift of leaders Chelsea, as Guardiola cut a forlorn figure on the bench.