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
Record signing Philippe Coutinho did not attend the game after completing his 142-million-pound ($192.67-million) move from Liverpool to Barca on Saturday although Ousmane Dembele made his first league start in more than three months.
Suarez struck his fifth goal in four games running by controlling a cross from Sergi Roberto and slamming the ball high into the net in the 38th minute.
Barca are nine points ahead of nearest challengers Atletico Madrid and 17 clear of champions Real Madrid, who were visiting Celta Vigo later on Sunday. ($1 = 0.7370 pounds)