Calgary got its game going 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.
"We had pretty much all four lines going and you need that if you want to win," Jokinen said.
Iginla put the Flames into the lead at 16:13 on a pretty setup by Alex Tanguay, who spotted the Flames' captain in behind the Buffalo defense.
"We've had these chances over the last four or five games and we just haven't been able to put them in," Iginla said. "Hopefully this is the start of a snowball in the other direction where we get those, and they find a way into the net."
Calgary tied the game 1-1 at 2:26 of the second period on Jokinen's eighth goal of the season.
Robyn Regehr's wrist shot through a crowd was kicked out by Miller, but Jokinen scored on the rebound.
Jokinen 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.
"The puck is bouncing my way a little bit now and I'm a big believer that if you work hard, and you keep doing things right, then eventually pucks are going to start going in," Jokinen said.
The Flames have won two straight and climbed within six points of the St. Louis Blues and the eighth and final playoff spot in the Western Conference.
"We looked really excited that last game and I think everybody's feeling it. We're in a situation where we have to be desperate and tonight was certainly a good win for us," Tanguay said.
The Flames will look to extend their winning streak to three on Friday when they host the Colorado Avalanche.
The Sabres, who conclude a two-game road trip to Alberta with a game Tuesday night in Edmonton, fell 10 points back of the final playoff spot in the Eastern Conference.
"We need to win," said Stafford. "It's come down to this where we need the points and it starts with tomorrow night. We just have to forget about this one and get ready for a big one in Edmonton."
The Sabres dressed a lineup with two significant holes from the one that suited up against Florida in their 4-3 loss before the Christmas break.
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 defenseman Tyler Myers, who came down with the flu.
"It's a little bit of a factor. Derek's our leading scorer and Tyler's one of our better D-men, not just even strength but on the power play as well," Stafford said. "At the same time, we need guys to step up, to fill in for their spots, especially Derek in the long term."
The Flames extended their lead to 3-1 at 2:20 of the third when Kotalik scored his first goal of the season. Moss then banged in a Tim Jackman rebound at 6:48 to put the Flames ahead by three.
"We got the lead and the next 40 minutes, some poor decisions on our part," Buffalo forward Jochen Hecht said. "We turned the puck over, they go the other way. We gave up 2-on-1s, 2-on-2s. We got lucky they were only up 2-1 after two."
Kiprusoff finished with 25 stops. Miller had 28 saves.
- 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 the past five meetings.