Calgary got going in the second period after falling behind 1-0 in a lackluster opening 20 minutes in which the teams combined for just 13 shots.
The Flames emerged from the first intermission skating much better and generating significantly more scoring chances, getting 14 shots on Buffalo goaltender Ryan Miller and taking a 2-1 lead.
Iginla put the Flames into the lead at 16:13 on a pretty set up by Alex Tanguay, who spotted Iginla in the open behind Jochen Hecht and sent a perfect breakaway pass to the Flames captain, who snapped a shot between Miller's pads.
Calgary tied the game at 2:26 of the second period on Jokinen's eighth goal of the season.
Iginla sent the puck back to Robyn Regehr at the blue line and the veteran defenseman wristed a shot through a crowd that Miller kicked out a pad to stop, but the rebound was fired in by Jokinen for his eighth goal on the season.
Jokinen, who also had an assist, is experiencing a resurgence back on the club's top line with Tanguay and Iginla. The four-time 30-goal scorer has six goals in his past nine games after a sluggish start to the season in which he scored twice in his first 25 games.
Alex Kotalik, David Moss and Tom Kostopolous also scored for Calgary (16-18-3). The Flames have won two straight. The Flames will look to extend their winning streak to three on Friday when they host the Colorado Avalanche on New Year's Eve. Calgary is 4-1 in its past five games at the Scotiabank Saddledome.
Drew Stafford and Patrick Kaleta scored for Buffalo (14-18-4). Buffalo concludes its short two-game road trip to Alberta with a game Tuesday night in Edmonton.
The Sabres used a lineup with two significant holes from the group that played against Florida in their 4-3 loss before Christmas.
Missing up front was leading scorer Derek Roy, who tore his quadriceps tendon against the Panthers and is lost for the season.
Absent from the blue line was 20-year-old defenseman Tyler Myers. While spending the Christmas break at his parents home in DeWinton, a small community just south of Calgary, last year's NHL Rookie of the Year came down with the flu.
The Flames extended their lead to 3-1 at 2:20 of the third when former Sabre Kotalik scored his first goal of the season, firing a shot into the top corner as he skated down the wing.
Moss banged in a Tim Jackman rebound at 6:48 to put the Flames ahead by three goals.
Miller was busy in the second period keeping the Sabres within striking distance despite allowing the two goals.
Iginla had a pair of chances 10 seconds apart only to have both his wrist shot and turnaround slap shot turned aside.
Two minutes later, Miller kicked out his toe to deny a shot from Rene Bourque.
Buffalo scored the lone goal of the first period on Stafford's 10th of the season.
Stafford eluded Matt Stajan as he cut in front of the Flames net then slid a pass across the crease, intended for Hecht. Instead, it banked off the skate of Flames defenseman Anton Babchuk and past Miikka Kiprusoff.
Kiprusoff finished with 25 stops. Miller had 28 saves.
Notes: Calgary won for just the second time when trailing after one period (2-8-2). ... Iginla is two assists away from 500 for his career... Calgary improved to 3-0-2 against Buffalo in its past five meetings.