It was the home side that opened the scoring after 12 minutes when Riera converted a low cross from Cejudo.
Play was interrupted for a significant period following the goal, however, when a stand at El Sadar collapsed, leaving a host of spectators on the field. However, it is understood that no serious injuries were suffered during the incident.
The match eventually resumed following a 30-minute break and Osasuna had their second after 14 minutes when Javier Acuna converted from close range.
Roberto Torres came close to making it 3-0 moments later, but his effort was blocked on the line.
Betis had the first real chance of the second period when Ruben Castro broke into the box, but his effort was straight into the arms of Andres Fernandez as the match continued to flow from end to end.
Javier Chica was next to come close for Betis after 55 minutes, but his effort once more brought the best out of Osasuna goalkeeper Fernandez.
Betis cut the deficit to 2-1 after 70 minutes, however, when Chica found the back of the net from distance.
It was so nearly 2-2 when Castro found space inside the Osasuna box moments later, but once more Fernandez was across to make a fine save and keep his side ahead.
Despite picking up the three points, it was not enough for the home side to survive as Getafe won at Rayo Vallecano.
Meanwhile, Betis' Segunda status has been confirmed for the last few weeks.