Their international backline of Takuya Iwata (Japan), John Irving (England), Marko Dordevic (Serbia) and Angel Berlanga (Spain) has been impenetrable.
Comfortable with the ball at feet and ironclad in their defensive work, they have rarely been troubled, and even have an eye for goal.
Irving, a 26-year-old centreback who was once on the books at Everton, showed quick feet and sharp awareness to bring the ball under control from a half-cleared corner in the 52nd minute, before rifling a low drive past the ES Setif goalkeeper to score the game's winner.
It was a game of few clear goal-scoring chances, but Auckland had the best of them. Striker Ryan De Vries blazed wide in the first half from outside the box and Angel Berlanga clipped the crossbar with a clever chip early in the second half.
"We controlled the game for 90 minutes," said Tribulietx.
"When we had the ball we were able to create three or four chances after we went 1-0 up, it really could have been 2-0. Overall I think we played the perfect game."
All Whites midfielder Tim Payne said that after the 120-minute extra-time marathon on Thursday, the players had to dig deep to overcome some painful barriers.
"Coming into the game the legs were still a bit sore, and mentally it's just been such an incredible effort from everyone," said Payne.
"After 45 minutes some of our legs were gone but we stayed strong, put our chance away and held on."
Tribulietx, who has proved himself a masterful tactical technician at the event, now has to plot a course to beat the best team in South America.
"We are now coming up against a very, very important team from Argentina. This game is going to be massive, massive - very, very difficult, and I haven't got more adjectives to add to that. But we are very happy with where we are at and very proud."
San Lorenzo, Pope Francis' favourite team, were seeded 15th in the knockout phase of the Copa Libertadores and earned their spot at the Club World Cup by defeating 16th seed Nacional in the final.
They are captained by experienced Colombian defender Mario Yepes.
Auckland City FC's next opponents:
• San Lorenzo de Almagro
• Based in Buenos Aires
• 15 league titles
• Stadium: Pedro Bidegain (43,494 capacity)
• Favourite team of Pope Francis
• Considered one of the 5 Great Teams ("Los 5 Grandes") in Argentine football, with River, Boca, Independiente and Racing
• Qualified for Club World Cup after winning the Copa Libertadores despite being 15th-ranked team going into knockout phase
• Finished 11th in Argentine Primera last season
• Former players: Jose Luis Chilavert, Pablo Zabaleta, Ezequiel Lavezzi
Club World Cup prizemoney
• Winner: $6.43 million
• Runner-up: $5.14 million
• Third place: $3.21 million
• Fourth place: $2.57 million
• Fifth place: $1.93 million
• Sixth place: $1.29 million
• Seventh place: $640,000.