Sevilla had the lion’s share of possession and created 22 goalscoring opportunities to Juve’s 13.
The match went to extra-time after a 1-1 draw made it 2-2 over two legs.
Substitute Erik Lamela headed in Bryan Gil’s cross on 95 minutes to end Juve’s chances of any silverware this season.
Juve's Dusan Vlahovic had struck on 65 minutes from Adrien Rabiot's assist but fellow substitute Suso levelled in fine style from distance in the 71st to force the extra 30 minutes.
AAP