Steen extended his scoring streak to 13 games, the longest for a Blue since Pierre Turgeon had a 15-game streak in 1999-2000.
The Blues won for the fifth time in six games despite giving up two short-handed goals on the same power play for the first time in more than 20 years. St. Louis last allowed that to happen on Oct. 8, 1992 against the then-Minnesota North Stars.
With the game tied at 2-2, Steen gave the Blues the lead for good at 6:20 of the third period. He took a long pass from Polak, broke in alone on right wing and beat Carolina goalie Justin Peters with a wrist shot.
Oshie added an empty-net goal at 19:16 for the final margin.
The Blues have scored first in their past 10 games, and did so again Saturday when Polak converted Chris Stewart's centring pass at 9:25 of the second period. Backes scored 2:11 later with a shot from a bad angle to make it 2-0.
It appeared that the Blues were in position to add to their lead when Carolina received a bench minor for too many men at 15:05 of the period. Instead, the Hurricanes scored their first two short-handed goals of the season to tie the game.
First, Staal sneaked between the Blues defence for a breakaway and beat Elliott with a backhand at 15:37. Less than a minute later, Elliott mishandled the puck along the right boards. Riley Nash stole it and centred to Gerbe and he put it in the vacant net at 16:34.
NOTES: St. Louis, which had played the fewest games in the league coming into Saturday (17), will play seven more times before the end of the month starting Sunday in Washington. ... Carolina's Alexander Semin, who was hit with a hard check by Alex Pietrangelo in the first period, later left the game with what was announced as an upper body injury and did not return. ... Blues coach Ken Hitchcock earned his 618th win, moving him past Jacques Lemaire and into sole possession of ninth place on the wins list.