The only goal in Seville was headed in by Brazil striker Luis Fabiano, on a centre from Diego Capel, in the 35th minute.
Spirited Osasuna came close to equalizing at the end, but the Sevilla defence managed to hold firm.
“These are three very important points for us,” said veteran Sevilla keeper Andres Palop.
“Now that we have taken back fourth place,” he added, “we intend to keep it, right until the end of the season”.
Sevilla are four points behind third-placed Valencia, who drew 1-1 away to Sporting Gijon on Saturday.
Palop and company are two points above Mallorca - who are away to lowly Tenerife on Monday - and four ahead of Deportivo Coruna, who crashed 2-0 away to lively Espanyol earlier on Sunday.
Joan Verdu and Jose Callejomn scored the goals which keep Espanyol well above the relegation quicksand.
“We have wasted a good chance today,” said Deportivo defender Alberto Lopo, who was playing against his former team.
“We need to be more consistent away from home,” he added, “in order to get close to the Champions League places”.
The defeat leaves Deportivo in sixth place, just two points above Athletic Bilbao, who lost 2-1 away to Villarreal on Saturday.
In Sunday’s other games, Getafe were held 2-2 by Almeria, while Malaga scored an important 3-0 win away to Racing Santander, which keeps them well above the danger zone.
Zaragoza also enjoyed a good Sunday on the road, battling out a 1-1 draw away to fellow strugglers Valladolid.
Xerez - who crashed 3-0 at home to second-placed Real Madrid Saturday - are well adrift at the bottom, with just 11 points. Then come Tenerife on 17, Valladolid on 19, Zaragoza on 21 and Almeria on 23.
Sunday’s late game brings together injury-hit leaders Barcelona and Atletico Madrid, who are sixth from bottom with 24 points.