The Spaniards had lived up to their billing as favourites following a blistering start and an early second-half double from Zlatan Ibrahimovic looked to have all but killed off the tie.
However Theo Walcott came off the bench to pull a goal back before Fabregas - who will miss the second leg at his old club after being booked - smashed in a late penalty after Carles Puyol was sent off for fouling the midfielder in the box.
While Barcelona will still be favourites to progress, Arsene Wenger's side again showed great character and could yet prove their doubters wrong once more with a similarly courageous display in the Nou Camp.
Arsenal were on the backfoot straight away in a frenetic opening, with Thomas Vermaelen cutting out a low ball into the six-yard box.
Goalkeeper Manuel Almunia - who had been at fault for Birmingham's stoppage-time equaliser on Saturday - was suddenly in the thick of the action as the Spaniard pulled off fine saves to deny Sergio Busquets and Lionel Messi.
The hosts just could not get hold of the ball - a situation so alien at Emirates Stadium.
Almunia was again called into action when he blocked Messi's drive following another mesmerising run by the Argentina international as the Gunners were simply outplayed at their own game, the home fans subdued as Wenger paced his technical area.
Then, Almunia denied Ibrahimovic from point-blank range and then spread himself in front of Xavi to save the follow-up before Messi's effort was blocked on the line by Alex Song, and eventually the ball hacked clear.
With quarter-of-an-hour gone, it continued to be relentless, one-way traffic from the Spaniards.
When Arsenal finally got some possession, Andrey Arshavin swung over a dangerous cross from the right before Samir Nasri cut inside from the left and drilled an angled shot across the face of goal and wide of the far post.
On 27 minutes, Arsenal were forced into a change when Arshavin was replaced by Emmanuel Eboue, as the Russian limped off.
Barcelona continued to look the more threatening as Ibrahimovic again shot over.
Nicklas Bendtner - who smashed a hat-trick against Porto to seal a place in the quarter-finals - was picked out by Nasri's left-wing cross. But the Dane could only fire his close-range effort against keeper Victor Valdes and the rebound onto the post. The assistant had already correctly flagged for offside anyway.
Three minutes before the break, defender William Gallas - just back from eight games out - had to be carried off after appearing to aggravate his calf problem. Song dropped back into the centre of defence, with Denilson coming into midfield.
Just before the break, Fabregas was penalised for a foul on Busquets, with Swiss referee Massimo Busacca showing a yellow card - which rules the Spaniard out of next week's return to his old club.
Then, disaster struck for Arsenal 30 seconds after the restart.
A long ball from inside the Barcelona half by Gerard Pique split the centre-backs, and Ibrahimovic raced clear down the right channel.
Almunia decided to come out, which invited the Swede to simply lob his shot up and over the keeper into the far corner.
The Gunners looked for a quick response when Fabregas sprinted down the right before releasing Gael Clichy on the overlap.
His cross was met by Bendtner, but the Dane could only power a header straight at Valdes.
It was, though, seemingly game over and indeed the end of the Gunners' European dream when, on 59 minutes, Ibrahimovic beat the offside trap as he latched onto Xavi's fine throughball, before drilling his shot past Almunia.
With 24 minutes left, Wenger made his final throw of the dice as he sent on Walcott for Bacary Sagna.
It proved an inspired move as the winger, under the watchful gaze of England manager Fabio Capello, latched onto Bendtner's pass on the right side of the box, before slipping the ball under Valdes.
With seven minutes left, the match turned when Barcelona captain Puyol barged into Fabregas as he tried to connect with a knockdown from Bendtner.
The referee pointed to the spot, before showing a red card. Fabregas lashed in the spot-kick to give his side hope at the Nou Camp.