Espanyol found themselves on the backfoot when defender Bernardo Espinosa was dismissed in the 16th minute for appearing to elbow an opponent while waiting for a cross.
The visitors initially coped well with the setback but were clinging on for most of the second half and it took two big interventions from goalkeeper Diego Lopez to thwart Getafe, including a double save in stoppage time.
Raiola meets PSG president to discuss Pogba move - Paper Round
The point took Espanyol off the bottom of the table and into 19th place on 24 points, two points from the safety zone. Getafe remain fifth on 47 as they again missed out on the chance to move into the top four having lost 2-1 at Granada last Friday.
Bacca gives Villarreal 1-0 home win over lowly Mallorca
The result lifted Villarreal two places to seventh on 44 points from 29 games, two behind sixth-placed Atletico Madrid who have a game in hand. Mallorca stayed 18th on 25 points as the defeat dented their hopes of avoiding relegation.
A darting run and cross from Samuel Chukwueze left Bacca with a simple tap-in from two metres at the far post in the 16th minute, after Mallorca's Idrissu Baba had rattled the crossbar with a thunderbolt from 30 metres at the other end.
The lively Chukwueze fired wide after a solo run shortly after the break and visiting goalkeeper Manolo Reina saved a Manuel Trigueros shot before Mallorca missed a gilt-edged chance to equalise.
Substitute Aleksandar Trajkovski's fine footwork and cross left Juan Hernandez unmarked at the far post but the forward sliced his shot wide from six metres with the goal at his mercy.
Home keeper Sergio Asenjo kept out a fierce Ante Budimir shot and Villarreal cleared the ball off the line in the closing stages as Mallorca piled on the pressure but were unable to find a way through.
Eibar relegated from La Liga with defeat at Valencia
Barcelona hit Getafe for five to keep pressure on Real and Atleti