Malaga, who had started the season without a win in seven league matches, made a positive start and forced Angel Fortuno into an early save to deny David Larrubia from close range.
However, Espanyol took the lead in the 13th minute when Bryan Zaragoza collected Javier Hernandez's pass, cut inside the defence and fired a precise finish into the bottom corner.
The visitors had chances to extend their advantage before half-time. Roberto Fernandez was denied by Alfonso Herrero, while Carlos Puga blocked Hernandez's follow-up effort to keep Malaga in the game.
Malaga pushed for an equaliser before the break, but Rafa Rodriguez's long-range attempt failed to trouble Espanyol enough to prevent the visitors from taking a narrow lead into half-time.
The hosts continued to press after the restart and came close to drawing level when Pablo Martinez's free-kick struck the crossbar.
Herrero then kept Malaga within reach by producing another important save to deny Fernandez, who was chasing his seventh La Liga goal of the season.
Despite their pressure, Malaga struggled to turn their possession into clear chances, with Fernando Calero and Martinez both firing over the crossbar.
Just when Espanyol appeared set to claim all three points, Malaga delivered a late blow. Substitute Nino connected with Rafita's cross and struck a superb volley in the final minute of stoppage time to snatch a share of the spoils.
The result extended Espanyol's unbeaten run against Malaga to 15 matches, with nine wins and six draws. However, the Catalan side missed an opportunity to secure only their third away victory in their last 15 La Liga trips.
