A display of similar dominance will now be required at Camp Nou, as Barca trail 2-0 from the first leg of their Copa tie.
Barca had initially lacked a focal point, playing a 3-5-2 formation without a natural striker, yet their unorthodox front two combined to great effect for the opener after 29 minutes.
As Messi dropped deep to collect the ball, Dembele tore away on the shoulder of the last defender and met a pinpoint pass to fire under Yassine Bounou.
That was the only moment of real quality in a low-key first half, but Barca twice in quick succession should have added to their advantage after the break.
Sergino Dest blasted against the post when the ball broke his way following a patent move, before Dembele raced away again and teed up Messi, who blazed over.
Clement Lenglet then had a header ruled out for offside, yet Messi settled any nerves as he played a smart one-two with Ilaix Moriba and prodded in the rebound when Bounou blocked his dinked attempt five minutes from the end.
Only an apparent injury to Ronald Araujo, 15 minutes after his return to action, put a dampener on Barca's day.