Pedro Rodriquez and David Villa scored doubles with midfielder Xavi also on target in the 10th successive win for the all-conquering champions which left them five points clear of Real Madrid at the top.
Real are at home to Sevilla on Sunday as they bid for a win to keep pace with their arch-rivals.
Barcelona went into the match at the Cornella-El Prat stadium expecting a tough battle as Espanyol had compiled a flawless seven wins in a row at home in the league.
But once Pedro had shot them in front after 19 minutes, set up by Lionel Messi, they never looked back.
Midfielder dynamo Xavi gave Pep Guardiola's side a 2-0 lead before the break and the pattern of dominance continued in the second half.
Pedro grabbed his second, again assisted by the brilliance of Messi, before Dani Osvaldo pulled one back for Espanyol.
But Villa rubbed it in with two late strikes as Barca scored five goals at Espanyol for the first time in their history.
Earlier, Villarreal stayed third with another impressive 3-1 home win over Real Mallorca at El Madrigal.
Villarreal made it 23 points from a possible 25 at home to move five points clear of Espanyol in fourth.
Spanish international winger Santi Cazorla gave the hosts the lead after 11 minutes, but Jonathan de Guzman equalized in the 27th.
Villarreal were ahead again through a Giuseppe Rossi penalty on 35 minutes and Brazilian international Nilmar notched his 10th league goal of the campaign to seal victory after the break. CNN
