The Blues went behind inside 33 seconds after Melanie Leupolz scored an unfortunate own-goal and it got worse from there.
Barcelona bagged three more before half-time as Alexia Putellas slotted a penalty, and Aitana Bonmati and Caroline Graham Hansen got in on the act too.
Chelsea put in a spirited performance during the second-half, refusing to roll over, but they were unable to stage an unlikely comeback.
Blues boss Emma Hayes named the same team who beat Reading Women 5-0 to win the Women’s Super League last week, but her side got off to a nightmare start in Sweden.
Barca came flying out the blocks and, after Lieke Martens struck the crossbar, Fran Kirby tried to clear the ball - but the clearance hit Leupolz and looped over goalkeeper Ann-Katrin Berger and into the net.
The goal set the tone for a frantic opening 10 minutes and Chelsea could have levelled through Pernille Harder, who squandered two good chances.
In the end, it was Barca who doubled their lead after 14 minutes when Leupolz was judged to have caught Jenni Hermoso in the box. Putellas made no mistake from the spot.
The Spanish side had their foot on the gas and they refused to take it off, carving Chelsea open twice more before the break to make it 4-0.
First, Bonmati was slid in to score and then Martens got in down the left and squared the ball for Hansen to put them four goals ahead after just 36 minutes.
Chelsea were much improved after the break, with Kirby in particular trying to somehow get them back into the match.
Barca, though, were able to keep them at arm’s length and with 25 minutes to go they were still 4-0 up.
Hayes threw on Beth England and Erin Cuthbert in one last roll of the dice.
Barca, however, saw out the game and in doing so won the Women’s Champions League for the first time in their history.