Hector Moreno gave the Catalans the lead early in the second half and Mubarak Wakaso made sure of all three points in stoppage time.
The result takes Javier Aguirre's side 13 points clear of the relegation zone but Osasuna, who are five points above the bottom three, still have some work to do.
Espanyol made the brighter start to the game and came close to taking the lead with less than four minutes on the clock.
Sergio Garcia hammered a powerful shot at goal which Osasuna goalkeeper Andres Fernandez managed to get a hand to and push against the crossbar.
Osasuna's best chance of the opening 45 minutes fell to Kike Sola, who found himself unmarked just yards from goal but inexplicably shot wide of the target following a cross from Miguel De Las Cuevas.
Both coaches had spoken of the importance of showing strength and aggression during the game, with Osasuna boss Jose Luis Mendilibar admitting his side stood little chance of winning the game through skill.
It was unsurprising, then, that little quality football was on offer, and it was somewhat predictable that the opening goal came from a set piece.
Wakaso sent a corner towards the near post and Moreno rose to head the ball just beyond the reach of Fernandez to break the deadlock.
Espanyol goalkeeper Kiko Casilla kept out Osasuna's best efforts in the second half, the first coming from Emiliano Armenteros and the second arriving as a powerful effort from De Las Cuevas which was destined for the bottom corner until Casilla got a hand to it.
Nino thought he had equalised in the 68th minute when he headed home a cross but the goal was correctly ruled out for a marginal offside.
With the final whistle approaching Espanyol launched a counter-attack as substitute Martin Petrov released Wakaso, who raced ahead of the Osasuna backline and towards the ball.
Fernandez rushed off his line but the Ghanaian got to the ball first, taking it beyond the reach of the keeper with his first touch before delivering a perfect left-footed shot with his second which landed in the far corner of the net.