Ernesto Valverde's side were allowed to score an equaliser after an error from Andreas Christensen gave Andres Iniesta an opportunity to assist Lionel Messi. Before their goal, Barcelona's only clear-cut chance came to Paulinho who headed wide when Messi made a decision to switch play and cross the ball across the Chelsea backline.
He fine-tuned his radar after the interval, however, rifling home into Ter Stegen's bottom-left corner to give Chelsea the lead.
Messi's goal means Chelsea must score in the return leg at the Camp Nou on March 14 to have any chance of progressing further in Europe's elite competition.
He may have fallen out with the board since winning the Premier League in May - but the 48-year-old coach still has the full support from the Chelsea fans.
It was Chelsea who broke the deadlock in the 62nd minute as Willian, who hit the post twice before the half time break, finally found the back of the net. "Tonight we were a bit unlucky". But we did not and the result is still open, we have to go there and try to win.
In the other, pre-quarterfinals played on the night, hosts Bayern Munich more or less booked their last eight spot with a crushing 5-0 win over Besiktas at the Allianz Arena in Munich.
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Students reportedly had to undergo searches of their backpacks and lockers before the school released them to their parents. A school official in OH says a middle school student apparently shot himself after bringing a gun to school.
Speaking to BT Sport after the final whistle, Ferdinand said: "Antonio Conte's face says it all - the disappointment".
"We were very close to playing a ideal game, we paid dearly for one mistake", said Conte.
Conte, who was happy with the way his team played, insisted that Barca's superstars will always make teams pay for their mistakes.
Fabregas said Chelsea must not defend in the second leg. "The effort of the players was great, we are talking about 1-1 and maybe we deserved more". They pressed us very high and made life hard for us. That was a performance of control, discipline and focused attacking, and they deserved to win even before Michy Batshuayi's added time victor.
"I think in the second leg we have to play a game against Barcelona and we know his team is very strong and fantastic".
"We will go there trying to win because we have to score and we will try to pull off the ideal game as we did today except for the small mistake that we made", added the Belgian.