After an underwhelming first half at Estadio do Morumbi, Coutinho scored twice within eight minutes of the restart to put Brazil in control on Friday.
A VAR check and handball led Coutinho to the penalty spot and the Barcelona star made no mistake in the 50th minute before making it 2-0 three minutes later after capping a sweeping move.
Everton came off the bench and scored the goal of the night with a blistering effort from outside the area in the 84th minute as the Selecao – who have won the Copa on each of the previous four occasions they have hosted in 1919, 1922, 1949 and 1989 – made a winning start in Group A.
Playing without superstar Neymar after he was ruled out of the tournament with an ankle injury, 2018 World Cup quarter-finalists Brazil dominated but struggled to create any real clear-cut chances.
Thiago Silva saw a header flash wide of the post and Casemiro came close with an audacious effort for Brazil, who had 77 per cent of the possession in the opening 45 minutes.
The half-time whistle was met by a chorus of boos around the stadium amid a subdued atmosphere as Brazil failed to impress against Bolivia – a nation in which they had won nine and drawn two of the past 11 games on home soil, scoring 46 goals and conceding just four times.
But a VAR check helped ease some of the tension and pressure with the ground after Adrian Jusino was adjudged to have handled the ball inside the penalty area.
Coutinho successfully converted the spot-kick before he completed a quick-fire double after latching on to Roberto Firmino's cross at the back post.
The result was never in doubt from that point as Brazil turned the boos into cheers in the south-west of Sao Paulo, where substitute Everton scored a stunning long-range goal with six minutes remaining.
What does it mean? Brazil up and running with 100th win
Seeking a ninth Copa title and first since 2007, Tite's Brazil got the job done in Friday's curtain-raiser. It was not perfect but the Selecao managed to claim their 100th Copa victory.
Coutinho takes centre stage
The Barcelona attacker struggled at Camp Nou in 2018-19, leading to speculation of a possible return to the Premier League via Chelsea or Manchester United. Coutinho, however, stepped up when Brazil needed him most with his first international brace since scoring a hat-trick against Haiti at the Copa America Centenario.
Improvement needed by Brazil
If the half-time boos were any indication, Brazil did not meet expectations prior to the break. Richarlison and Roberto Firmino were virtually non-existent in the first half, while Coutinho and David Neres struggled to make an impact. The Selecao did beat Bolivia but they will be punished against better opposition if they do not improve.