Reuniting with the team to conquer them in last year's semi-finals and the 2020-21 showpiece, Emma Hayes's side produced a defensive masterclass and condemned the hosts to their first defeat of the season through Erin Cuthbert's first-half strike.
A slice of European history was also made by Chelsea, who became the first English team to win a first leg of a Women's Champions League semi-final, while also ending Barcelona's magnificent five-year unbeaten run on home soil stretching back to February 2019.
The Blues remarkably did not face a single shot on target throughout the first leg, although two-time Ballon d'Or Feminin winner Alexia Putellas wasted a golden chance to deny the visitors a famous success right at the death.
Prior to next Saturday's return fixture at Stamford Bridge, Barcelona have a top-flight trip to Levante Las Planas on Wednesday evening, whereas Chelsea have a full week's worth of rest to enjoy.
Cuthbert clinical as Barcelona bemoan penalty decision
Boosted by the presence of captain Millie Bright, on the bench for the first time since sustaining her serious knee injury in November, Chelsea put in an early defensive display which the Euro 2022 winner would have been proud of.
Hayes's trio of centre-backs were hardly allowing Barcelona a sniff, although Aitana Bonmati nearly engineered a chance for Salma Paralluelo in the 17th minute, but the 20-year-old's shot was deflected over.
After weathering the early Barcelona storm, Chelsea began to force the issue in attack, and the Women's Super League champions stunned the Catalonian crowd with six minutes of the first half remaining.
Sjoke Nusken was the instigator, holding up the ball brilliantly with Barcelona shirts around her and teeing up skipper Cuthbert, who shifted the ball onto her right foot and curled a sublime strike out of Cata Coll's futile reach.
The Blues' lead would seemingly come under threat just six minutes into the second period, though, as Patricia Guijarro went for a carbon copy of Cuthbert's strike, which hit the outstretched arm of Kadeisha Buchanan.
Stephanie Frappart pointed to the spot straight away, but while Mariona Caldentey was standing over the ball waiting for the green light, Frappart was belatedly sent to the pitchside monitor to review the incident.
Buchanan was under pressure from Paralluelo as she blocked Guijarro's strike with her arm, and the Barcelona attacker was deemed to have been interfering with play from an offside position, leading to Frappart overturning her decision.
An aggrieved Barcelona - who soon brought on Putellas - were yet to fashion a single shot on target as the game entered its final 20 minutes, and Chelsea's Mayra Ramirez could have put the first leg more or less out of sight in the 76th minute, but she fired over after holding off two Barca defenders.
Jonatan Giraldez's side, who were becoming increasingly agitated, were handed nine minutes of additional time to try to find the leveller, but the clock had ticked over to 100 minutes by the time Lucy Bronze nodded Paralluelo's last-gasp free kick into Putellas's path.
The Spaniard ostensibly only needed to find the target to salvage a draw, but from just a few yards out, she curled a close-range attempt wide as Barcelona's best chance of the game went begging.