Borja Iglesias and Wu Lei threatened but failed to hit the target early on for the hosts before Esteban Granero put them ahead after 20 minutes with a free-kick which found the top corner of the net.
LaLiga's bottom club responded well to the setback and Enric Gallego and Ezequiel Avila both worked Diego Lopez in the Espanyol goal before half-time.
Huesca were level at the start of the second half when Xabier Etxeita converted Jorge Pulido's assist from a set-piece.
The visitors continued to attack and Avila twice went close before Wu Lei nearly restored Espanyol's lead but his shot from a tight angle struck the near post.
Both teams had chances to win it late on. The best opportunity perhaps fell to Espanyol's Mario Hermoso in injury time but the defender's header was straight at the goalkeeper.
Victory would have put the hosts within four points of the top six, while Huesca are five points adrift from safety as they fight to stay in the top flight.