The Flames are in a much less enviable position now.
Dallas seeks its sixth victory in seven games Sunday when it visits the fading Flames, who have lost five of six.
The Stars had lost four straight to Calgary and three in a row overall to slip to 11th place in the Western Conference -- two spots behind the Flames -- prior to their meeting in Dallas on Feb. 16. But Mike Ribeiro scored in overtime to give the Stars a 3-2 victory, sending the teams in opposite directions heading into this matchup.
A seven-point swing in the standings has Dallas (34-26-5) leading 11th-place Calgary (29-25-11) by four, with the Stars currently in playoff position. Dallas' win last month began a 6-1-2 stretch, while the Flames' defeat started a 2-3-3 slump.
The teams also will meet in a potentially crucial home-and-home series March 24 and 26.
The Stars had only 15 shots on net, but they limited the Oilers to 20, with Kari Lehtonen missing a shutout by 30 seconds.
Coach Glen Gulutzan said Lehtonen, 4-0-1 with a 1.37 goals-against average over his last five starts, has been a major reason for the current run.
"It was not our best outing, but we have to take points wherever we can get them right now," Gulutzan said. "We have a good goaltender and we need to use him. This is how we've had success. This is the way it has got to be done if we want to get into the playoffs."
Lehtonen made 25 saves last month against the Flames, who let at least one point slip away Friday after allowing the game-winner with 46 seconds remaining in a 3-2 loss to Anaheim.
"Really unacceptable with where we're sitting (in the standings) right now," said Michael Cammalleri, who had an assist.
Coach Brent Sutter was frustrated by the final goal and said such breakdowns can't happen during a tight race for a postseason spot.
"It's a tough way to lose a game, especially (because) it's big points we let get away from us," Sutter said.
The Flames have gone 0-2-2 in their last four at home, getting outscored 18-9 in that span.
Miikka Kiprusoff got the night off Friday but will likely be back in net for this contest. He made 29 saves in Thursday's 4-2 win at Phoenix, though he has a 3.95 GAA during Calgary's home skid.
Kiprusoff made 29 saves last month versus the Stars, but despite the defeat is 5-1-2 with a 2.06 GAA in his last eight starts against them.
Dallas has won three straight on the road while outscoring opponents 9-2. Lehtonen, though, has lost both of his career starts in Calgary with a 4.04 GAA.
The Stars had won five of six road meetings in the series before the Flames took both at the Scotiabank Saddledome last season.
AccuScore has powered more than 10,000 simulations for every NHL game on ESPN.com, calculating how each team's performance changes in response to game conditions and opponent's abilities. Each game is simulated and the game is replayed a minimum of 10,000 times to generate forecasted winning percentages.