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
Liverpool took a fifth-minute lead through a Keita shot which deflected off Porto midfielder Oliver Torres and beat the helpless Iker Casillas.
Firmino doubled the advantage in the 26th minute -- Jordan Henderson split the Porto defence with a superb pass to Trent Alexander-Arnold, whose low cross was tapped in from close range by the Brazilian.
Moussa Marega then had a low drive well saved by the legs of Liverpool keeper Alisson Becker and the Portuguese side did well to stay in the game in a scrappy second half to give themselves a chance of a comeback at home in next week's second leg.