The South American champions were expected to make light work of Auckland's amateurs in the semi-final but they required extra time to win 2-1 at the Stade de Marrakech on Wednesday.
Despite a sluggish performance, San Lorenzo were on track for a showdown with European champions Real Madrid after Pablo Barrientos volleyed the opener two minutes before half-time.
Auckland deservedly equalised in the 67th minute through Spanish full-back Angel Berlanga, which threatened to inspire a remarkable upset by the New Zealanders.
But San Lorenzo were not to be denied in Marrakech, with substitute Mauro Matos dispatching a loose ball in the box in extra time.
"We're delighted we achieved our aim of reaching the final," Bauza was quoted as telling FIFA.com afterwards.
"It was a difficult match against a side that was very well-organised defensively. We didn't play well in the first half; we were nervous and didn't show enough determination. On top of that we gave the ball away too often.
"The game didn't pan out as planned for us, which is why I made some changes. After that we were able to get into it better.
"Now we'll start preparing for the final and will do everything we can to win.
"We'll try to play to the best of our ability and to meet expectations, even if we are going up against one of the best teams in the world with a lot of quality individuals."
Auckland coach Ramon Tribulietx had nothing but praise for his players, who earned countless admirers following their exploits at the Club World Cup.
"We're the moral victors. We had the chance to win the game in normal time," Tribulietx said.
"My players are obviously devastated because we came so close to winning.
"We're very proud of the way we played today and we'll remember it for a long time."