Ávila couldn't beat goalkeeper Joel Robles one-on-one after Osasuna launched a 6-on-2 counterattack following a botched set piece by Betis just before halftime. He also hit the crossbar early in the second half.
Osasuna beat Leganés in its opener and has strung together four draws, including 2-2 against defending champion Barcelona. The hosts were left in seventh place before the rest of this weekend's matches.
Betis is 13th after keeping its first clean sheet of the season. Betis next hosts Levante on Tuesday, while Osasuna visits Real Madrid on Wednesday.
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