Melanie Leupolz inadvertently put the ball past her own goalkeeper after just 35 seconds, and a penalty from Alexia Putellas followed by strikes from Aitana Bonmati and Caroline Graham Hansen had Barcelona four goals clear before half-time.
English champions Chelsea were expected to pose a major threat to the Barcelona goal, but key forwards Fran Kirby and Sam Kerr had an off night in Gothenburg.
Barcelona were able to cruise through the second half and become Spain's first winners of the competition, putting a 4-1 defeat to Lyon in the 2019 final firmly behind them.
On that previous occasion, Barcelona trailed 4-0 after 30 minutes, but this time it was Chelsea who suffered from the early onslaught against impressive Spanish league champions.
Lieke Martens hit the bar with a powerful shot from the edge of the penalty area after just 20 seconds, and as Chelsea scrambled to clear, Kirby booted the ball against the shin of team-mate Leupolz, resulting in it looping over goalkeeper Ann-Katrin Berger and into the top left corner.
Barcelona boss Lluis Cortes watched his team attack with verve and great movement, winning a penalty when Leupolz clipped Jennifer Hermoso. Putellas converted and Barcelona were two goals clear after 14 minutes.
Putellas then picked a pass that released Bonmati to toe in the third, and it was 4-0 after 36 minutes when Graham Hansen buried a close-range chance after Martens dashed down the left and away from Niamh Charles before crossing low across goal.
While Barcelona celebrated, their victory removed the possibility of Chelsea winning both the men's and women's Champions League titles in the same season.
After Emma Hayes' team fell short, Chelsea will hope Thomas Tuchel's men avoid such a sour experience in the men's final on May 29 when they face Manchester City.
Hayes told BT Sport: "Today was difficult because the game was over before it began. That's what is so difficult to reflect on. The damage was done.
"I'm proud of the second-half performance. Congratulations to Barcelona. They're worthy winners and deserving of their title.
"They were favourites for a reason and you have to stay in the game against this team.
"The early goal and the manner in which we conceded it, and the penalty. Once you get a 2-0 lead in these games ... I felt everything fell for them. They got the rub of the green. They made that happen. They're a wonderful team and deserving winners."