With the win, the Catalan giants leapfrogged now third-placed Sevilla, who destroyed Malaga by the same scoreline on Saturday.
And it was the former Liverpool striker who put Luis Enrique’s side ahead in sensational fashion on 18 minutes.
In full stride, the Uruguay international expertly brought down a pinpoint long ball from Andres Iniesta before cutting inside the last defender and sliding his right-footed shot past a sprawling Diego Lopez and into the far corner.
Suarez then struck again just after the hour mark for his second of the day — pouncing on Lopez’s spilled save attempt of a Lionel Messi shot and powerfully burying the rebound.
With the floodgates open, Barca found a third seconds later through Jordi Alba who fired his shot low and past Lopez after a slaloming Messi run ended with the ball rolling into his path.
Espanyol worked a consolation goal in the 79th — David Lopez striking sweetly into the top corner after a Gerard Moreno pass from a counter-attack. But Barca worked their fourth just moments before the final whistle — Messi poking past Lopez from close range after a fine one-two with Suarez at the top of the box — to complete the rout at the Camp Nou.