First-leg goalscorer Caroline Graham Hansen broke the deadlock after 63 minutes but Guro Reiten quickly levelled from a rebound after Sam Kerr was denied.
In front of over 72,000 fans, the 2021 winners held on to reach a fourth final in five years.
Chelsea showed plenty of grit to stay in the tie against a superior Barca, becoming the first side to stop them from winning in a home match all season across all competitions.
Barcelona were without England defender Lucy Bronze after knee surgery, while Ballon d'Or winner Alexia Putellas was on the bench for the first time this season after her ACL injury last July.
However the Spanish star was not risked as a substitute in a tense and hard-fought game which went down to the wire.
Graham Hansen thought she had fired Barcelona ahead again early on but the strike was disallowed as she used her arm to control the ball.
Nigeria international Asisat Oshoala slashed wildly off target when well placed as the hosts dominated the ball but struggled to find the opening goal.
Aitana Bonmati showed fantastic footwork in the area but could not find the net, as Barcelona gave the Blues a lesson in possession football but not finishing.
Graham Hansen danced across the box early in the second half but had her route to goal blocked as Jonatan Giraldez's side continued to control the match.
Eventually the Norwegian winger pounced after a fine burst downfield by Aitana Bonmati, who played in Graham Hansen to finish clinically.
Chelsea conjured an instant response when Erin Cuthbert won the ball with a powerful tackle on Mariona Caldentey, allowing Melanie Leupolz to release Kerr.
Barcelona goalkeeper Sandra Panos thwarted the Australian striker but Reiten was on hand to finish as the ball bounced her way.
Panos fielded a swerving Cuthbert drive from distance as Chelsea sought a goal to force extra-time, with Emma Hayes' side finally on top.
Barcelona sought to kill the tie on the break and substitute Salma Paralluelo came close with a low strike tipped away by Ann-Katrin Berger.
Brazilian striker Geyse missed a good opportunity for Barcelona in stoppage time as the hosts kept Chelsea at bay and celebrated wildly with their fans at full-time.
Barcelona will face either Arsenal or Wolfsburg in the final in Eindhoven on June 3.
