The match in Konya saw two Istanbul giants open the season in a battle for one of Turkey's prestigious cups.
Besiktas, winners of the 2015-2016 league campaign, began the match by testing its arch-rival's defense on several occasions.
The team found numerous opportunities to go in front but Galatasaray's Uruguayan goalkeeper, Fernando Muslera, had other ideas, leading to a scoreless first half.
The other side of halftime began as Besiktas kept up the attack on Galatasaray’s goal, with forward Cenk Tosun missing a clear chance on goal in the 54th minute.
But with an unlucky Besiktas side missing chances, the Turkish Cup winners also failed to seize its opportunities to take the lead.
In the 72nd minute, Galatasaray's flamboyant left-winger Armindo Bruma dribbled past defenders but his cross was caught and held by goalkeeper Tolga Zengin.
Besiktas, again in the 88th and 90th minutes, was unable to convert chances, ending regular time with a goal.
In the extra time, thanks to a classy cross from Wesley Sneijder, defender Hakan Balta made the most of his opportunity to shine for Galatasaray with a header in the 100th minute, into Besiktas' net.
It was all Galatasaray needed but it was unable to hold onto the lead when in the 107th minute, defender Aurelien Chedjou scored the equalized with an own goal.
In the penalty kick phase, Galatasaray made successfully converted three straight kicks, while Besiktas fell short on each try.
With the victory, Galatasaray secured its fifth Turkish Super Cup in the team’s last seven occasions. The Lions also have bagged 10 of the last 15 local cups in Turkey.