The former Villarreal and Real Madrid boss was presented in Malaga on Friday following the sacking of Jesualdo Ferreira earlier in the week, and will not take over the team until Sunday.
Malaga's B team coach Rafa Gil was left in charge for the trip to Barcelona, but there was little he could have done about Javi Marquez's stunning 30-metre strike within minutes of the start.
Espanyol maintained their 100 percent home record, despite being under pressure during the second half, and climbed to fourth with 18 points from 10 matches, five short of Real Madrid.
Malaga notched their seventh match without a win in all competitions and remained 18th with seven points.
"We have a very good squad. I'm sure we'll get things sorted out and that we'll start getting positive results very soon," Malaga's French striker Nabil Baha told Spanish radio.
"Pellegrini only arrived on Friday and he's not had time to tell us what he wants yet. He will take charge on Sunday and then he can speak to us as a team and individually about his philosophy."
HIT CROSSBAR
Earlier, Real Sociedad striker Joseba Llorente scored after seven minutes to give the promoted Basque club a 1-0 home win over Racing Santander that pushed them up to sixth with 16 points.
Espanyol took an early lead against Malaga when Marquez picked up the ball in midfield turned inside his man and cracked in a fierce drive from outside the area.
Malaga slowly came back into the game and they dominated after the break.
With five minutes to go Quincy Owusu-Abeiye crashed a shot against the Espanyol crossbar from almost exactly the same place as Marquez had scored in the first half, but the tiring hosts held on for the victory.
Pellegrini's first test at the helm will be to try and keep Malaga in the King's Cup when they host promoted Hercules on Thursday defending a 0-0 first-leg scoreline.
