Oviedo came from a goal down to win 3-1, 3-2 on aggregate, with the final goal arriving in extra-time through Francisco Portillo.
A delighted Paunovic declared afterwards: "We did it!
"I want to give a lot of credit to the previous coaching staff, who worked very hard, and when we took over the team, there was a lot of very good work done.
"This also goes for Dubovsky, for Radomir Antic..."
Paunovic also said: "I want to enjoy this. I've had a thorn in my side for 24 years. I haven't seen my family for three months, and today they're here. They understood that I had to dedicate myself to something that transcends us and repair the emotional damage.
"Oviedo is back where it deserves to be: for the fans, for the city, for its history... Things have been done well. Last year we were close