Barcelona, who rested Lionel Messi and Luis Suarez and also had Gerard Pique and Ivan Rakitic on the bench, went ahead through Paco Alcacer's header.
Arnaiz, the 22-year-old, drafted into the side after impressing for Gerard Lopez's B team, fired home the goal of the game after Alcacer and Gerard Deulofeu had put the holders in control at the Nueva Condomina.
Barcelona have won the competition in each of the last three seasons and play the second leg at the Nou Camp on Wednesday, 29 November.
Ernesto Valverde's side, who are four points clear at the top of La Liga, have now won 12 and drawn one of their last 13 games in all competitions.
Barcelona are next in action on Saturday with an away league game at Athletic Bilbao.
