On Friday, the Barcelona attacker netted twice inside five minutes before substitute Everton put the result beyond doubt with a long-range strike at Sao Paulo's Morumbi Stadium, reports Xinhua news agency.
Despite the comprehensive scoreline, the five-time world champions were below their best against an organised if unthreatening Bolivia outfit.
For long periods, Brazil lacked a cutting edge in the absence of star forward Neymar, who was ruled out of the tournament last week because of an ankle injury.
"It was a tough match for us," Coutinho told reporters after the game. "At half-time, the manager (Tite) asked us to focus more and to control the ball better. We managed to do that. The first goal changed the course of the match."
Brazil dominated possession early but struggled to find ways past a resolute Bolivia defence. Roberto Firmino and Thiago Silva had early chances from corners while Coutinho failed to make clean contact with a header after a Filipe Luis cross.
Tite opted against making changes at half-time and his faith was rewarded almost immediately. Argentinian referee Nestor Pitana consulted the video assistant referee before ruling that Adrian Jusino used his left hand to obstruct Richarlison's chipped shot. Coutinho then dispatched the resultant spot-kick into the bottom left corner.
The goal quickly released the pressure on Brazil and the Selecao netted again four minutes later when Coutinho headed in after a precise cross from his former Liverpool teammate Firmino.
Everton, introduced as an 85th-minute substitute for David Neres, completed the rout with a fine solo goal, five minutes from time.
The Gremio forward cut in from the left before smashing a low drive from the edge of the box that curled into the bottom right corner of Carlos Lampe's goal.
( With inputs from IANS )