Midfielder Andres Iniesta said the incident had buried any suspicions of a rift between the Real Madrid and Barcelona members of the squad, following the recent acrimonious clashes between the two clubs.
"We're all fighting for the same cause and we're all team-mates, there's no doubt whatsoever about that," Iniesta told reporters after Spain's controversial 3-2 win.
"There was a war at the end of the match, but peace was declared between the Real Madrid and Barca international players, who stood up for each other," it said.
"Madrid and Barca players were involved in another flare-up, but this time on the same side," it added, before launching into a detailed explanation of how Barcelona's Sergio Busquets entered the melee to defend Real Madrid's Alvaro Arbeloa.
Iniesta scored Spain's first goal and set up the second for Fabregas, who also scored the winner from a rebound after his own penalty had been saved.
"Iniesta is the most simple and efficient player I have seen," Chile coach Claudio Borghi said.
"It was a pleasure to watch him play. He is elegant and makes the difficult things look easy."
"It has been a long time since I have been so happy and I have to see now if I get some playing time with the national team and if I can make the most of it," he said.
"Sometimes in these friendlies we find it tough to get into the game."
