The former Wigan Athletic striker scored his 12th goal of the season with a last-gasp effort to help Samet Aybaba's side wrap an impressive result at the Medical Park Stadium.
Just before the first half break, Hakan Arslan gave the visitors the lead and Kone, brought on for Congo striker Thievy Bifouma with six minutes left in the game, added the second goal.
The ex-Everton marksman now has 12 goals in 29 league appearances in his maiden campaign in Turkey.
The result saw sixth-placed Sivasspor, now with 44 points, close the gap between them and their hosts who are just above them to
Aybaba's men host Genclerbirligi in their next league encounter on April 28.