The visitors' frustration grew with every wasted chance and coach Javier Aguirre was sent from his dugout to the stands midway through the second half after protesting a decision by referee Ignacio Iglesias Villanueva too vehemently for the official's liking.
Osasuna began the day occupying the final relegation spot but move up to 15th in the Primera Division table thanks to the win, with Real Valladolid slipping down to 18th.
Alvaro Cejudo scored the only goal of the game after 33 minutes as Osasuna edged the first half, but the hosts were also indebted to goalkeeper Andres Fernandez for a string of quality saves as Espanyol put up a fight in the second period.
Espanyol, meanwhile, stay in 10th place but their miserable away run continues - they have taken just eight points from nine matches on the road this season.
Osasuna forward Emiliano Armenteros fizzed a free-kick just wide of the right-hand post with only a few minutes on the clock and then Lolo had the first attempt on target, testing Kiko Casilla.
Cejudo also came close to grabbing the opener, shooting just wide of the goal from the edge of the area, while David Lopez had the visitor's best attempt of the first 45 minutes, forcing an excellent save from Fernandez.
Not long after the half-hour mark, the hosts got the goal their initiative had deserved, even though they enjoyed a touch of fortune.
Cejudo ran onto a mis-hit clearance by Javi Lopez and cut inside before slamming the ball beyond the reach of Casilla.
The hosts had two further chances to score before the break but Casilla saved well from Joan Oriol and then Miguel de Las Cuevas.
Espanyol had been timid in the first half but were bolder after the break.
Fernandez had to race off his line to prevent Jhon Cordoba getting on the end of a through-ball, and then the Colombian shot wide of goal when Sergio Garcia was better placed to score.
Armenteros had squandered a great chance to double the lead shortly after the re-start but as time ticked on, Espanyol became more and more dominant.
Fernandez made further saves from David Lopez and Abraham, while Joan Capdevila headed over the bar, and in stoppage time Iglesias waved play on when a cross appeared to hit Oier on the arm, to the fury of the Espanyol players.