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
A masked Diego Costa, who broke his nose in training, slotted Chelsea in front after five minutes and the Blues were three ahead with 17 minutes on the clock after Pedro and Willian punished lackadaisical Newcastle defending.
Newcastle staunched the goal flow until the hour mark when Cesc Fabregas's pass sent Pedro away to make it 4-0 before Bertrand Traore added a fifth.
Andros Townsend grabbed a late consolation for Newcastle.