Pablo Sarabia put Sevilla ahead when the video assistant referee gave a goal which had been ruled out for offside.
But Gerard Pique levelled from close range and Ousmane Dembele then fired Barca into the lead.
Sevilla had a late penalty when Ter Stegen fouled Aleix Vidal but he held Wissam Ben Yedder's weak spot-kick.
Barcelona have taken part in nine of the last 10 Super Cups, but this was the first to take place over just one leg and in a foreign country.
Sevilla, under new boss Pablo Machin, were impressive and led after Sarabia received Luis Muriel's pass and placed it past the goalkeeper early on - with a goal eventually awarded following a VAR review.
Barca equalised late in the first half when Lionel Messi's free-kick hit the post and the back of goalkeeper Tomas Vaclik, and Pique turned home the rebound into an empty net.
Sevilla then hit the crossbar from Franco Vazquez's looping header as both sides pushed for victory.
But it was Dembele who sealed the game when he lashed a shot home from 20 yards via the underside of the crossbar in the 79th minute.
There was more action to come, with Ben Yedder's miserable penalty, but Barca - who handed debuts to Clement Lenglet, Arthur and Arturo Vidal - win for the sixth time in nine years.
Source: bbc.com
BDST: 1133 HRS, AUG 13, 2018
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