The English Premier League side turned in a gritty performance to deny the Spanish champions and managed to keep World Player of the Year and competition top scorer Lionel Messi quiet to boost their chances of making next month's final.
A large slice of good fortune also helped inflict only a third defeat this season on Barca, who dominated possession, hit the bar and the post and had a Cesc Fabregas effort cleared off the line by Ashley Cole.
Barca coach Pep Guardiola, whose side host bitter rivals and fellow Champions League semi-finalists Real Madrid in La Liga on Saturday, acknowledged that Chelsea, chasing a first European crown, were now favourites to progress.
However, he said recovering from the one-goal deficit and eliminating the Londoners was a "great challenge" he and his players were happy to accept.
"I don't expect Chelsea to attack or pressure us high up the pitch but to deploy 10 players in their half and look to counter-attack," Guardiola, bidding to lead the Catalan club to a third Champions League title in four years, told a news conference.
"They will probably hold back and try to look for their chance," the former Barca and Spain midfielder added.
"We must not forget that Chelsea, with very little, can be an extremely dangerous opponent and they do what they do exceptionally well.
"We just need to find a way of creating goals."
Barca had 72 percent of possession and 19 attempts on goal at Stamford Bridge compared to four for Chelsea but striker Didier Drogba proved more clinical than the visitors' forwards when he slipped away from his marker and fired low past goalkeeper Victor Valdes moments before half-time.
Playmaker Andres Iniesta, who had a claim for a penalty waved away by the referee in the first half, said Barca would seek to be more effective in front of goal on Tuesday.
"We have the feeling that we created a lot of clear chances but we were just lacking the goal," he told reporters.
"We were on the wrong end of a defeat and we need to up our game significantly," added the Spain international, who scored the dramatic late goal that knocked Chelsea out on away goals in the 2009 semi-finals.
"The team is capable of doing that. It's not just a matter of luck."
