Visiting centre-half David Brekalo was left unmarked as he headed home Eduard Atuesta’s free-kick with just seven minutes gone.
Winger Ivan Angulo doubled City’s lead in the 29th minute with a powerful low drive into the far corner from just outside the penalty box.
France legend Antoine Griezmann marked his debut following the 35-year-old forward’s move from Atletico Madrid by firing home from just inside the box three minutes after the break as Gunn was left exposed by a loss of possession.
Paraguay midfielder Braian Ojeda completed the rout in the 73rd minute as his header squeezed between Gunn and the near post from another Atuesta set piece.
At the other end, Gunn’s opposite number, Canada’s Maxime Crepeau, produced several fine saves, a couple denying Timo Werner a scoring debut for San Jose after the Germany striker’s move from RB Leipzig.
Despite the defeat, Gunn’s side remain tied on points at the top of the Western Conference but second on goal difference behind Vancouver Whitecaps, who lost 4-3 away to Cincinnati but have a game in hand.
San Jose are fourth in the overall table, with Nashville leading ahead of Argentina forward Lionel Messi’s Inter Miami.
Gunn’s side next host LA Galaxy, who are ninth in the Eastern Conference, on Sunday.