Juventus were without Cristiano Ronaldo, who tested positive for COVID-19 on Oct. 13, meaning a matchup pitting the Portuguese against Lionel Messi for the first time since 2018 would have to wait until at least the second group encounter.
Barca problem child Ousmane Dembele got the start alongside Messi and he rewarded Ronald Koeman's faith early on with a goal from outside the penalty area to give the visitors the lead.
Juventus looked dangerous at the other end of the pitch as well and had the ball in the back of the net through Alvaro Morata right before 30 minutes, but the flag had gone up for offside and the goal was disallowed.
The teams returned from the half-time break with Barca still up 1-0 and Koeman making one change, substituting Ronald Araujo for Sergio Busquets due to an apparent injury.
Morata once again looked to have put Juventus back on level terms with a close-range strike, but once again the Spaniard was adjudged to have been offside after the match official consulted with VAR as Barca clung to their lead.
Barcelona continued to look dangerous in the attack, with Messi flashing a shot wide of the left post from the top of the area just after the hour mark and Pedri seeing his close-range attempt blocked minutes later.
Koeman made another change in the 66th minute, bringing on youngster Ansu Fati for Dembele with the Frenchman still working his way back to full match fitness.
The hosts' hopes of getting back in the game took a big hit in the 84th minute when Merih Demiral was sent off after receiving a second yellow card to leave Juve with only 10 players to the match.
Messi then put the game away from the penalty spot after Fati was hauled down in the box to reach the final scoreline.
Barca were rocked on Tuesday when club president Josep Maria Bartomeu resigned to avoid facing a vote of no confidence after some 20,000 fans signed a petition demanding that he step down.
"The best answer was today's game. We want to win titles and matches as we showed today," said Sergi Roberto. "It's all in the past, we're concentrating on our job."
Koeman agreed that his team had tried to put the boardroom issue out of their minds.
"I think we have to concentrate on the sporting side," he said. "It doesn't affect us and it doesn't worry me. We put our energy into football."
Meanwhile, Juventus coach Andrea Pirlo said the defeat will be used as a lesson and will help his side grow.
"It was a difficult game against a team that knows how to play and are further down the path than we are. We are a team under construction, with players who were playing only their second Champions League match," the first-year manager said.
Captain Leonardo Bonucci admitted that results so far were disappointing.
"It's time to grit our teeth, to bring out the best in ourselves. These results are not up to our standards. Tonight, we knew it would be difficult. We made too many mistakes and Barcelona don't forgive," he said.
"We could have done something more... but obviously, there is a lack of experience at European level in the players who have arrived."