Barca were 3-0 up by half-time, Robert Lewandowski scoring his 20th league goal of the season before Alejandro Balde, 19, doubled the lead.
Lewandowski added the third before Jules Kounde’s header made it 4-0.
Espanyol did reduce the deficit through Javier Puado and Joselu but remain in trouble near the bottom of the table.
Barcelona have 85 points, 14 more than nearest rivals Real Madrid, with 12 points left to play for.
It is their first La Liga title since club legend Lionel Messi left in August 2021 and first since Xavi was appointed manager in November 2021.
Meanwhile, Espanyol are in danger of a second relegation in four seasons from La Liga after a ninth league defeat in 11 games.
They are four points from safety with four matches left.
Source: soccanews.com