Jairo Samperio opened the scoring midway through the first half with a fine individual goal, and Carlos Bacca doubled the lead from the penalty spot just before half-time in a highly controversial incident, which saw Osasuna coach Javi Gracia sent away from his dugout for protesting the decision.
Javier Acuna scored a fine goal for Osasuna in injury time, but it only served as a consolation for the Navarrans.
The victory sees Sevilla move on to 47 points and cement their bid to qualify for Europe again, while Osasuna, on 29 points, remain in danger of relegation.
Sevilla boss Unai Emery criticised the decision to play the game just 60 hours after his players had run themselves into the ground to defeat Betis on penalties, but the visitors showed few signs they were still feeling the effects of their exertions, playing with far more intensity than Osasuna.
Jairo broke the deadlock on 27 minutes, receiving the ball on the right wing, cutting into the area and turning a defender before striking a low shot into the bottom corner of the near post.
Fabricio Fazio then nearly scored a second, heading just over the bar and onto the roof of the net after reaching a cross before Osasuna goalkeeper Andres Fernandez could.
The game then began to slip away from Osasuna's grasp in three frantic minutes at the close of the first half. First Damia Abella came agonisingly close to equalising, arriving at the far post to volley just wide of the near post. Sevilla then launched an attack, Vitolo racing past Osasuna players down the right wing and then squaring to Jairo, who had an open goal to aim at.
However, the winger inexplicably struck the crossbar, holding his head in his hands in despair at the miss. His blushes were saved when the referee gave a penalty a couple of seconds later, Damia falling to the floor after clashing with Vitolo, his hands landing on the ball as he hit the ground. Osasuna insisted Vitolo had fouled Damia, but the decision stood, and Bacca sent Andres Fernandez the wrong way to score.
Sevilla goalkeeper Beto was substituted at half-time and replaced by Javi Vargas, whose first task was to prevent Bacca from scoring an own goal, tipping a header from the Colombian over the bar following an Osasuna free-kick.
Bacca then had three chances to score at the correct end in the space of four minutes, but squandered them all, first sending the ball over the bar, then hitting the outside of the post, and then denied by Fernandez.
Osasuna were unable to create many chances of note until Acuna dribbled from the corner flag into the box and past three defenders to blast into the net, but the goal, coming in the 94th minute, had arrived too late to impact on the result.