Both teams had opportunities to register in Seville, but Sarabia's 58th-minute effort and a late Ben Yedder strike has given Sevilla a two-goal advantage to take into the second leg at Camp Nou next week.
Kevin-Prince Boateng only joined Copa del Rey holders Barcelona on loan from Sassuolo on Tuesday, but the 31-year-old went straight into the Catalan club's starting XI, operating at the tip of their attack.
Barcelona had more of the ball in the first 15 minutes, but there were no opportunities to report as Sevilla sat a little deeper in the early stages of the first leg.
Eventually the first shot of the match arrived in the 17th minute, but Ivan Rakitic's attempt from distance was always sailing over the home side's crossbar.
Jesus Navas was Sevilla's biggest threat down the right in the opening 25 minutes, but the winger's radar was off when it came to the final pass, with Barcelona clearing their lines on a number of occasions.
Sevilla's best chance of the first half came in the 36th minute when Ben Yedder evaded the challenges of a number of Barcelona players before looking to find the top corner, but his effort was just too high.
Barcelona came close five minutes later when Malcom drove into the Sevilla box before rounding Juan Soriano, but the Brazilian, who has been linked with a move away from the club, could only find the side-netting.
The final opportunity of the first period came for Ben Yedder after Sergio Escudero had delivered a fine low cross into the Barcelona box, but the striker saw his close-range attempt thwarted by Jasper Cillessen.
A lively start to the second period saw both teams have good possession of the ball.
Boateng came close to meeting a deep cross from Alena in the 47th minute, while Sevilla were causing issues down the other end, with Navas and Ben Yedder the home side's main threats.
Ibrahim Amadou had a super chance to send Sevilla ahead just before the hour after meeting a low Navas cross inside the Barcelona box, but the 25-year-old's effort just missed the post.
Sevilla did make the breakthrough in the 58th minute, however, when Sarabia fired a Quincy Promes cross into the back of the net from inside the Barcelona box.
Pablo Machin's side came close to doubling their lead moments later when Banega met another super delivery from Promes, but the Argentine's header was just too high.
Coutinho should have levelled moments after entering as he found himself free inside the Sevilla box, but the Brazilian's powerful attempt was too high.
Instead, it was Sevilla that scored the game's second goal in the 76th minute when Ben Yedder turned a low Banega strike into the back of the net from close range.
Both teams had opportunities to register in the final 15 minutes, but 2-0 was how it finished, leaving Barcelona with plenty to do in the return match at Camp Nou next Wednesday.
SEVILLA (3-4-3): Soriano; Gomez, Kjaer, Mercado; Escudero (Arana 88'), Banega, Amadou, Navas (Silva 71'); Promes, Sarabia (Vazquez 67'), Ben Yedder
BARCELONA (4-3-3): Cillessen; Roberto, Pique, Lenglet, Semedo (Alba 80'); Rakitic, Arthur, Vidal; Alena, Boateng (L Suarez 63'), Malcom (Coutinho 63')