In a first half devoid of invention it was an error that gifted Espanyol the lead as Dudu Aouate collided with one of his own defenders and dropped the ball invitingly at Vladimir Weiss' feet for the Slovakian to slot home.
Aouate's day got even worse two minutes after the break as he was harshly sent off for bringing down Rui Fonte just outside the area.
Despite being down to 10 men Mallorca took the game to Espanyol for most of the second period and the hosts had keeper Kiko Casilla to thank for all three points as he denied Marvin Ogunjimi and Gonzalo Castro with fine saves.
Espanyol coach Mauricio Pochettino had stressed the importance of getting Los Pericos' shocking midweek cup defeat to Mirandes out of their system and they started by far the better of the two sides.
Rui Fonte passed up the first clear chance of the game as he ran onto Ndri Romaric's fine through ball but shot straight into the body of Aouate.
Three minutes later though the hosts were in front as Aouate lost the ball after clashing with Pablo Caceres and Weiss took full advantage to score his third goal of the season.
Mallorca's chances appeared to have gone when Aouate was sent off just two minutes into the second half, despite clearly taking the ball before any contact with was made with Rui Fonte.
However, after Weiss had struck the resulting free-kick against the post and Raul Rodriguez somehow failed to put away the rebound, it was the visitors who had the better chances.
Casilla brilliantly denied Ogunjimi his first goal for Mallorca with a flying save from the Belgian's header before making a more routine stop from Victor Casadesus.
Javi Lopez should have wrapped the points up for Espanyol when he shot straight at Juan Calatayud with five minutes remaining, but Mallorca continued to press and were denied again by Casilla in stoppage time as Castro's drive was beaten away by the keeper and just evaded Ogunjimi on the follow-up.