Mauricio Pochettino's side put in determined performance to frustrate Pep Guardiola's charges which leaves Real Madrid five points clear in the title race
The away side dominated possession throughout the match, but were unable to capitalise on Fabregas' goal and Mauricio Pochettino's men stayed determined until the end to earn the draw.
The hosts made a bright start, and almost took the lead within the first five minutes when Sergio Garcia clipped a cross to the back post for Joan Verdu, and the former Barcelona man headed towards goal only for Victor Valdes to make an excellent diving save. Verdu smashed the rebound towards goal but Gerard Pique was on hand to make a heroic clearance off the line.
Barca thought they had taken the lead in the 13th minute when Cristian Alvarez passed the ball straight to the feet of Messi and the Argentine squared the ball for Fabregas to slot home. However, the referee spotted a handball from Messi, and the goal was disallowed.
It took just three minutes for Pep Guardiola's side to score another, and this time it counted. Dani Alves made a typical run down the right wing and stood a cross up on the edge of the box for Fabregas, and the former Arsenal man powered a header into the bottom corner, with some question marks over the goalkeeping of Alvarez.
The visitors had another disallowed goal just before the hour mark when Dani Alves collected an inch perfect pass through the middle from Xavi before taking the ball around Alvarez and slotting home, but the Brazilian was correctly ruled as offside.
The champions came close to extending their lead in the 76th minute through a Lionel Messi chance. The Argentine somehow dug out a shot on the byline and hit the post with a right-footed attempt from an impossible angle.
Espanyol's grit and determination paid off when they managed to grab an equalising goal in the 85th minute. Raul Rodriguez drove down the right wing and crossed to the near post where Thievy flicked the ball on into the centre and Alvaro was perfectly placed to head home and send the home fans into raptures.
The last few minutes proved to be incredibly dramatic as Pique struck the post with a left-footed shot and Pedro's rebound appeared to be cleared off the line by the arm of Raul Rodriguez, but no penalty was given.
Barcelona now trail Real Madrid by five points in the title race and remain in second position. Espanyol move on to 24 points and find themselves eighth place in La Liga.