Ousmane Dembele produced an extraordinary individual move on the half an hour mark, when he went past a couple of Celta players before teeing up Memphis, who opened the scoring for the hosts.
Marc-Andre Ter Stegen made a solid save to deny Thiago Galhardo six minutes later and Barcelona doubled their lead through Aubameyang before the break.
The Blaugrana converted their first chance in the second half into a goal through the former Arsenal striker, with Dembele registering yet another assist.
Celta bounced back instantly and pulled one back through Aspas, but Jeison Murillo received a straight red card after bringing down Memphis outside Celta's box.
Xavi later said: "Honestly it was not a good game, we didn't play well. After the red card we played well, we had passion, but 11 vs 11 we suffered.
“It's a very important win, especially when you don't play well. At least we competed. We need to keep going, this is not the way but at least we won."
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