Pockets of fans threw flags and bottles at police at a major roundabout in the city, while revellers of all ages, decked out in red, white and blue, whistled and cheered for their side following their 2-1 loss against Spain.
As many as 50,000 people swarmed onto the main road that runs through Santiago to celebrate, local media estimated.
The post-match unrest had been quelled but more detentions could follow, said police, who have now made mass detentions in Santiago after each of the side's three World Cup games.
Friday's match comes almost four months after a devastating earthquake hammered south-central Chile and killed more than 500 people, and many Chileans feel the team's progress has lifted the national spirit.
"We are incredibly proud of what the Chilean players are doing," Pinera said, clutching a national flag. "I want the team to know that they have the hopes of a nation resting on them, a nation that has suffered greatly from an earthquake and tsunamis."
"This time, history will be changed because the Chileans deserve it," he said.
"It doesn't matter, we're happy anyway," she said. "We're in the World Cup, and we're showing that we can do it. It's helping the people who suffered most from the earthquake to be happy, and it unites us as a country."
