Frenkie de Jong and Robert Lewandowski put the Catalans in front before a lengthy stop in play due to an illness in the crowd saw the players go off the field before returning to play out the final 10 minutes.
"The game is secondary at the moment, but it was an important win at a difficult place to come," Barcelona coach Xavi Hernandez told Spanish TV. "We created a lot of chances, dominated the game and it's three points to keep in touch at the top of the table."
Xavi named a much-changed side from Barca's 5-1 midweek Champions League triumph over Viktoria Plzen and, one Raphina shot that hit the post aside, they rarely troubled the hosts in the first period.
Lewandowski, who came on as a substitute after the goal, continued his fine start to life in Spain with Barca's second 25 minutes from time to put the visitors in command.
As the game reached its conclusion there was a more than 50-minute stoppage to treat the ill fan before play could resume, with Fati and Dembele putting the gloss on the scoreline.