St. Louis jumped past both Los Angeles and San Jose into fourth place in the Western Conference, a spot that carries with it home-ice advantage in the first round of the playoffs.
The Blues have 58 points, and the Kings and Sharks have 57 apiece. All of those teams will play their final game of the regular season Saturday.
Reaves added a goal 2:10 into the third, giving him four for the season. Brian Elliott made 18 saves for St. Louis, which has won five out of six.
The Flames need to win their final game of the campaign to reach 20 victories for the season. Joey MacDonald allowed all four St. Louis goals on 20 shots.