The Nigeria forward extended his tally in the competition to four goals on his fourth appearance for the Turkish Super Lig club on Thursday
Qarabag kicked off on a flying note with Abdellah Zoubir opening the scoring for the hosts at the Basaksehir Fatih Terim Stadium in the eighth minute.
His opener separated both teams for the majority of the first-half but Kone got the equaliser for Sivasspor from the penalty spot, five minutes before the break.
After the restart, Uro Matic restored the lead for the Azerbaijan giants in the 55th minute, however, it did not last long as Kayode made an instant impact after replacing Casimir Ninga in the 57th minute.
A minute after his introduction, the former Manchester City striker brought the two teams on level terms again with his effort, courtesy of an assist from Yasin Oztekin.
The Nigeria forward has now scored four goals in the Europa League group stage this season, having notched at least a goal in each of his last three appearances in the competition.
Towards the closing 10 minutes of the encounter, Kone linked up with Ugur Ciftci to secure all three points for the visitors with his second goal of the night.
The 37-year-old forward played the entire duration alongside his compatriot Max Gradel while Mali’s Mamadou Samassa was in between the sticks for Sivasspor.
Qarabag, on the other hand, had Ghana forward Owusu Kwabena on parade but he could not add to his tally of a goal after five games.
Thursday’s victory left Sivasspor in the third spot in Group I with six points after four matches, a point behind second-placed Maccabi Tel Aviv while Qarabag languish at the bottom, and they are yet to pick a point after four matches.