The New Zealand amateurs defied the odds for the second consecutive match, upstaging African champions ES Setif 1-0 in Saturday's quarter-final in Rabat.
After overcoming host club Moghreb Tetouan of Morocco via a penalty shootout in a play-off, John Irving helped extend Auckland's dream run with a second-half goal.
Irving showed great composure to get away from his defender before firing the ball past Setif goalkeeper Sofiane Khedaira seven minutes after half-time.
Auckland are now just one win away from a possible match against European champions Real Madrid, with Copa Libertadores champions San Lorenzo standing in their way.
"We played extremely well and created a lot of chances, and really the only the thing missing was a second goal," Tribulietx was quoted as telling Auckland's official website.
"I'm really proud of my players. To put in a performance like that against the winners of the African Champions League, after a really tough 120 minutes in our first game, is just unbelievable."
Tribulietx added: "I'd like to say thank you to the Moroccan fans that supported us so well here today - that was brilliant.
"We've played two games and not conceded a goal yet, and now we’re in the semi-finals of the Club World Cup. It's just fantastic and a reward for all the hard work that’s being done by the entire club at Auckland City."
