Barca said before the game that Pedro wanted to leave the club but the 28-year-old came on to win the trophy, just as he did in 2009, pouncing on a rebound from a Lionel Messi shot.
Messi had himself scored a double with two stunning early free kicks while Rafinha and Luis Suarez also netted for the Catalans, who led 4-1 with just over half an hour left.
Barca's fifth triumph in the competition, which means they have now won four trophies this year, moved them level with AC Milan on the all-time Uefa Super Cup winners list.
“I got the goal but it was down to the work of the team and I am happy with the win,” said Pedro. “When you know you may leave it is difficult. I was angry about not starting the game but as always I tried to be professional and go out and help.”
Ever Banega had given Europa League winners Sevilla the lead with a free-kick after three minutes but Messi stamped his mark on the game with stunning free-kicks after seven and 16 minutes.
The Argentine's double for the Champions League holders means he is again joint record scorer in European competition with Real Madrid's Cristiano Ronaldo on 80 goals.
Rafinha slotted home a Luis Suarez pass just before the break and the Uruguayan scored himself after the restart having been found by Sergio Busquets to put Barca firmly in command.
Sevilla, though, fought back with goals from Jose Antonio Reyes, after 57 minutes, and Kevin Gameiro, with a penalty in the 72nd, before Yevhen Konoplyanka equalised with 10 minutes left to force the game into extra time.
“We went out looking to be creative and to cause danger,” Sevilla coach Unai Emery told a news conference
“To get to European finals you need to earn respect and so attack the opposition which is what we did.
“I don't think that we got the reward we deserved from the game. We had clear chances at the end and Barca were looking worried.”
With Neymar out due to mumps, Barca coach Luis Enrique chose Rafinha ahead of Pedro in attack but three minutes into extra time the Canary Islander got his chance and made the most of it.
Pedro fired the winner into the roof of the net from close range with five minutes left as Barca stayed on track to win six trophies this calendar year on the back of last season's treble.
Pedro also came off the bench in the 2009 Super Cup final against Shakhtar Donetsk to score in the 115th minute and secure a 1-0 victory for Barca after they had won their first treble.
“We knew that this would be a difficult game and this really showed the merit of the team. It is difficult to win trophies and games,” the Barca coach said.
I am very happy with the way that we won and showed the hard work that is necessary.
“We didn't know what to expect and it shows what you have to do to win a trophy.
“It was great for the fans and after 50 minutes it looked as though the game was over but against a rival like that you never know.” – Reuters
Original source: Barca, Sevilla in nine-goal thriller