After spotting the Sabres a 1-0 lead in the initial frame, Jokinen netted his eighth goal, batting in the rebound of a Robyn Regehr slap shot to tie the score 2:26 into the middle period.
Iginla put the Flames ahead for good 14 minutes later, scoring on a 2-on-1 break with Alex Tanguay.
Miikka Kiprusoff stopped 25 shots to earn the win.
Drew Stafford and Patrick Kaleta tallied for the Sabres and Ryan Miller made 28 saves in the team's first game since leading scorer Derek Roy was lost for the season with a torn left quadriceps.
Celebrity Families of 2014 [PHOTOS]