Brereton, making his first start for the country of his mother's birth, scored after 10 minutes when he slotted the ball home from 15 metres to complete a swift counter-attack.
Chile should have scored more against a Bolivia side that have won only three of their last 32 internationals but one goal was enough for the three points and top spot in Group A.
Brereton also forced Bolivian goalkeeper Carlos Lampe into at least two other good saves in the first half alone and was a handful for the Bolivian defence before being substituted in the 83rd minute.
Bolivia lost their opener 3-1 to Paraguay on Monday and they were without five players who tested positive for COVID-19, including top goalscorer Marcelo Martins.
Friday night's task proved too much for the depleted side against a rival team that won this tournament twice in a row in 2015 and 2016.
Even against a team missing injured striker Alexis Sanchez they could only muster three shots on target compared to Chile's 11.
Eduardo Vargas had the ball in the net in injury time for Chile but the second goal was ruled off due to offside.