TJ Brodie scored, and Mike Smith made 27 saves for the Flames.
With Calgary's loss, the top two teams entering the Stanley Cup Playoffs have been eliminated in the opening round for the first time since the NHL expansion of 1967-68. The Tampa Bay Lightning, who won the Presidents' Trophy, were swept in the Eastern Conference First Round by the Columbus Blue Jackets.
Since 1967-68, when six teams were added to make the NHL a 12-team league, there have been a number of playoff formats: division-based, conference-based, and for two seasons (1979-80, 1980-81) the top 16 teams were seeded by regular-season points.
In none of those instances had the top two teams in each division or conference, or the teams with the two best records, been eliminated in the first round of the playoffs.
"Everybody that makes it in is an NHL playoff team and they deserve to be in there," Smith said. "It's a hard season to get into the playoffs. It's so competitive. Once you're in there, anything can happen.
"I didn't think we played our best consistently throughout this series and you have to do your best if you want to move on. You can't move on just being average. They were better. They were the better team and they deserve some credit."