Former Liverpool striker Nabil El Zhar broke the deadlock in first-half stoppage-time and Los Amarillos struck further goals after the interval through Jonathan Viera, Pedro Bigas and Wakaso Mubarak.
Morocco international El Zhar opened the scoring with a low shot from an acute angle after Viera's pass inside the penalty area on the stroke of half-time after both sides had been guilty of missing chances.
Willian Jose's long-range effort forced a fine save from Espanyol goalkeeper Giedrius Arlauskis soon after the break before Viera doubled Las Palmas' lead in the 49th minute when he had time enough inside the box to despatch a low shot into the bottom corner.
Viera was the provider again as Las Palmas made it 3-0 seven minutes later when his free-kick was headed home by Bigas.
Mubarak's left-footed shot was brilliantly saved by Arlauskis in the bottom corner but the home side were out of sight in the 75th minute when the same player lashed the ball high into the net after a half-cleared corner.
Espanyol went close to a consolation when Hernan Perez's low effort in the 89th minute was inches wide, while team-mate Burgui had earlier seen his shot well saved by Las Palmas goalkeeper Raul Lizoain.
