For Betis, the Europa League offers momentary respite from a domestic relegation battle and La Liga's basement club looked to be relishing the stage as it took a 15th-minute lead at Estadio Ramon Sanchez Pizjuan.
Atletico Madrid-owned forward Baptistao headed in an inviting cross from Juanfran, but the hosts generally controlled the remainder of the opening period, with goalkeeper Antonio Adan keeping Betis ahead.
Sevilla dominated proceedings after the break but still struggled to find a way past Adan, and Baptistao wasted a glorious chance to double Betis' lead in the 54th minute.
A few moments after Kevin Gameiro had headed over from close range, Salva Sevilla netted against his former side to secure the visitors' third win at their bitter rivals since 1996.
Most of the buildup to the fixture focused on Betis' last two trips to Sevilla — in which it conceded a total of nine goals — and the visitors almost suffered a nightmare start.
Just 17 seconds in, Carlos Bacca burst past Jordi Figueras and into the penalty area, but his left-footed effort was saved by the feet of Adan.
The visitors capitalized on that let-off and took the lead after quarter of an hour. Baptistao produced an expertly timed run to get in front of Federico Fazio at the near post to power home a header from Juanfran's right-wing cross.
Sevilla nearly hit back five minutes later as Ivan Rakitic picked out Bacca with a precise lofted pass into the area, but Adan denied the Colombian again, palming his header away.
Both sides spurned glorious chances within one minute just after the hour mark as Cedrick saw his header well saved by Beto, before Vitolo poked Jose Antonio Reyes' cross agonizingly wide.
Betis should have doubled its lead in the 54th minute as Baptistao pounced on Fernando Navarro's slip before shooting straight at Beto.
Halftime substitute Gameiro nearly restored parity two minutes later after a clever turn in the area, but his effort went narrowly wide of the bottom-right corner.
With Sevilla pressing for an equalier, Betis looked threatening on the break and a last-ditch tackle by Fazio prevented Baptistao from doubling his tally, before Gameiro headed over an open goal from just a few yards out.
Salva then silenced the home fans with 13 minutes left as he turned on the edge of the area before rifling an unstoppable shot past Beto, rounding off the win for Betis.
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