Cristiano Ronaldo scored a pair of penalties either side of Weston McKennie's volley as Juve were again able to celebrate on the Camp Nou pitch.
Serie A champions Juve had visited Barca in the 2017 semi-finals and drew 0-0 to successfully defend a 3-0 aggregate advantage.
But despite the relative weakness of opponents Barca this time, the win was of particular note as the first time the Blaugrana had lost at home in the Champions League since 2013.
That statistic was put to Bonucci, although Lionel Messi's absence in that 3-0 reverse at the hands of Bayern Munich – the superstar was an unused substitute – was also referenced.
Not since going down 2-1 to Rubin Kazan in 2009 had Barca lost at home in Europe with Messi in the side.
Bonucci told Sky Sport: "We had a great desire to achieve this feat beyond the historical relevance.
"We had already come here a few years ago and brought home a 0-0 after winning the first leg 3-0. This one is even more beautiful.
"It was a great team effort and when you go out on the pitch with this nastiness, with this desire to sacrifice yourself and with a player like Cristiano, who is a sure-fire sniper, we were sure to do this kind of game.
"But I repeat: it was a great team effort. Now we recover, we have to think about the match in Genoa on Sunday, because even in the league we have to repeat performances like this."
Juve are fourth in Serie A but were good value for their victory despite having just eight shots – to Barca's 20 – and 41.1 per cent of the possession.
Bonucci, who was required to make only a pair of clearances and a single tackle, added: "We brought home the first place, which was important not only for the remainder of the Champions League but for ourselves, for this group [of players].
"It cultivates within us the awareness and belief that playing matches in this way we can do great things."