Trailing 3-2 entering the final frame, the Blues exploded for the three straight scores, triggered by Steen's equalizer 58 seconds into the period.
Pietrangelo added an insurance tally, and T.J. Oshie chipped in a goal and an assist for Blues, who won for the ninth time in 11 home games and moved into second place in the Central Division.
Jaroslav Halak stopped 28-of-32 shots to earn the victory.
Derick Brassard provided a goal and an assist, and Fedor Tyutin added three assists for Columbus.
Mason finished with 28 saves.
Swim Week Miami Beach 2014 [PHOTOS]