Madrid took the lead in the first 45 minutes with Marco Asensio's terrific debut effort, chances from Daniel Carrico followed but it was Franco Vazquez who brought Sevilla level.
Zinedine Zidane's side had the better of the chances in the early proceedings of the second period, with Isco and Karim Benzema coming close, but a penalty from Yevhen Konoplyanka looked to have secured the Super Cup for Jorge Sampaoli's side, but a late Sergio Ramos header took it the distance.
The first period of extra-time was dramatic to say the least with Timothee Kolodziejczak's dismissal and Ramos's disallowed goal. The second period didn't follow to the same tune, and looked to be heading to penalties, but Carvajal's solo effort secured the victory right at the death.
Making a mark
Asensio had been impressive on loan with both Mallorca and Espanyol, but had yet to make his professional debut for Madrid, but when given the chance, he certainly disappoint opening the scoring at the Lerkendal Stadion.
A seemingly harmless deflection fell to the feet of the 20-year-old, but he showed great technique pushing towards the edge of the area before curling beyond Sergio Rico and into the top corner.
Sevilla began to creep into the match as the half went on, and had a decent opportunity just before the half-hour mark.
Carrico looked to emulate Asensio's success, especially in distance, as he tried one from outside the area. The low effort bounced in front of Kiko Casilla, but the ''keeper did well to palm it away.
Sevilla had been knocking on the door as the half entered it's latter stages, and were rewarded with their equaliser in the 41st minute.
A chipped ball in from the wing was well take on the chest by Vitolo, however the ball got away from the striker, but it fell perfectly for Vazquez who fired low into the bottom corner on his competitive debut for Sampaoli's side.
Madrid almost regained their almost instantly, Lucas Vazquez showed great trickery to get to the by-line before flicking the ball into the box, he found Isco but his header was straight at Rico.
Looking for the breakthrough
Madrid fell flat as they came out for the second period, but had the better opportunities to regain their lead. Vazquez looked to cause havoc once again as he got to the by-line, he looked to set up an easy opportunity for Alvaro Morata, if not for the excellent back-heeled clearance from Nicolas Pareja.
Isco showed great trickery just before the hour mark, turning away from the defender but the Spaniard's curled effort was just wide of the post.
Looked to have sealed the win
Despite been under the quash for the majority of the second period, Sevilla looked to have snatched the win, after securing a penalty twenty minutes from the end.
Vitolo showed great trickery to wriggle his way into the area and looked to get beyond Ramos, but was clipped by the defender and referee Milorad Mazic had no hesitations.
Konoplyanka had only just got onto the pitch, but made no mistake as he coolly sent Casilla the wrong way to give Sevilla the lead.
Snatched away at the death
Sevilla were moments away from another European trophy, as Madrid piled everything forward, and Ramos showed his importance once again as he equalised late on.
Vazquez had proved a problem all game, and was at it again in the 93rd minute as he got to the by-line, his chipped ball reached the back post and the unmarked Ramos was there to nod home.
Sevilla were at a serious disadvantage at the beginning of extra-time, as they were reduced to ten men.
Vazquez was at it again with his lightning trickery, and it proved too much for Kolodziejczak, who had only been booked in the 89th minute, as he was given his marching orders for his high tackle.
Ramos thought that he had given his side the lead once again, as his diving header went underneath Rico, but the goal was flagged up, but the decision remains a mystery.
Keeping his side in it
The numerical disadvantage certainly came into play in the second period of extra-time, but Rico pulled off some excellent stops to keep his side in it.
James Rodriguez produced an excellent cross for Vazquez, but his shot was smothered by Rico. The keeper was then on hand to collect Rodriguez's ferocious volley moments later.
Victory sealed in style
The game looked destined for penalties, but Madrid have a tendancy to seal European victories in the final moments, and that didn't change here.
Carvajal turned defence into attack instantaneously, dispossessing Konoplyanka before charging down on Sevilla's area. The full-back did brilliantly to weave into area before toe poking home the winner.