The Catalan club started the day level on points with Atletico Madrid but ahead in the standings thanks to a superior head-to-head and goal difference.
However, Atletico was downed 2-1 at already relegated Levante meaning it slips back to third position behind city rival Real Madrid which overcame Valencia 3-2 at the Santiago Bernabeu.
Barca now has a one point lead over arch-rival Real atop the table going into the final round of fixtures and can no longer be caught by Atletico.
"We deserve the league title and I hope we can be precise in the final game to win," Barca boss Luis Enrique said after the match in comments carried by Barcelona's official Twitter account.
Enrique's men have been operating on the assumption that there is no room for error in recent weeks.
And Lionel Messi eased any nerves at an overcast Nou Camp Sunday by opening the scoring for the home side early on with a spectacular free-kick.
A brace from top-scorer Luis Suarez shortly after half-time made sure of a vital three points before substitute Rafinha added a fourth on 73 minutes when Espanyol goalkeeper Paul Sabata fumbled a tame Neymar cross.
Neymar then got his name on the score sheet after unselfish play by Suarez left the Brazilian striker with a tap-in.
Atletico experienced a far more testing afternoon against Levante despite taking an early lead through a Fernando Torres strike.
Victor Casadesus equalized for Levante just before halftime with a bullet header after slack Atleti defending.
And as the visitors pushed for the winner that would keep the pressure on Barcelona, Giuseppe Rossi netted after a swift breakaway to end all hopes Atleti had of notching a second La Liga crown in three years.
Real hangs on
That result means Real Madrid is now the only team that has any chance of stopping Barcelona.
It saw off a determined Valencia at the Santiago Bernabeu 3-2 with the visitors finishing the game with 10 men.
Cristiano Ronaldo opened the scoring for Real midway through the first half before Karim Benzema finished from close range to double the advantage just before halftime.
Rodrigo pulled a goal back for Valencia at the start of the second period but Ronaldo restored Real's lead on the hour mark.
Andre Gomes made it 3-2 with a rocket shot from outside the area after 81 minutes before Rodrigo saw red shortly after.
Real will now travel to Deportivo la Coruna next weekend with the knowledge that a victory allied with a Barcelona slip-up will see provide its first La Liga crown since 2012.