Albin bundled the ball in after Real failed to clear a corner in the 88th minute, and Barca can extend their lead over their arch-rivals to 13 points in the late game if they can overcome second-placed Atletico Madrid at the Nou Camp.
Jose Mourinho's team are third with 33 points from 16 games, four behind second-placed Atletico. Espanyol are 19th with 12.
Karim Benzema was left in the stands with an ankle injury, and Cristiano Ronaldo started in the centre-forward position, but for all their possession they struggled in the first half.
Espanyol silenced the home crowd when striker Sergio Garcia, a Euro 2008 winner with Spain, sprinted clear to net past Iker Casillas in the 31st minute.
Luka Modric crashed a shot against the post, but just as the Bernabeu was getting restless Sami Khedira crossed and Ronaldo stuck out a foot to level in the 45th minute.
Ronaldo's reverse pass picked out Fabio Coentrao's driving run into the area, and the Portugal defender put Real ahead with his first league goal for the club, soon after the re-start.
A fingertip save and the woodwork prevented a quick third for Real, but they were living dangerously and substitute Albin struck near the end, and the team left the pitch to whistles.
Earlier, Rayo Vallecano scored a late penalty to spoil Ernesto Valverde's home debut as Valencia coach, with a surprise 1-0 victory.
Valverde was brought in as a replacement for the sacked Mauricio Pellegrino two weeks ago and has overseen victories away at Osasuna in the league and in the King's Cup, but his side offered little for the demanding Mestalla crowd.
After an evenly-balanced contest with few chances, home defender Tino Costa needlessly hauled down Roberto Trashorras in the area for a penalty in the 83rd minute.
Rayo's Alejandro Dominguez stepped up to score from the spot, and the home fans whistled and chanted against club president Manuel Llorente in the closing minutes.
Valencia's objective is a return to the Champions League, where they have already reached the last 16 this season, but they lie seven points adrift of fourth-placed Malaga in 11th place with 21 points.
City neighbours Levante were above them in fifth with 27 points after a 1-0 win at Real Zaragoza earlier in the day.
Juan Ignacio Martinez's side gained a measure of revenge for their defeat by the same scoreline at home to Zaragoza in a King's Cup last-16 first leg during the week.
Ruben Garcia gave the visitors the lead after 19 minutes and their notoriously solid defence stood firm thereafter.