Mats Sundin had two goals and an assist, and Bryan McCabe added a goal and an assist for Toronto, which blew a 3-1 lead in the third period but pulled away for its second straight victory since snapping a season-worst seven-game losing streak.
About three minutes after Carolina tied it 3-3, the Maple Leafs worked the puck to Steen in the right slot and he snapped it past Cam Ward from about 15 feet away.
The Hurricanes pulled Ward in the final minute but couldn't convert in the closing moments against Andrew Raycroft.
Erik Cole, Justin Williams and Mike Commodore scored for Carolina, which lost its fifth straight.
Raycroft made 29 saves for Toronto, which snapped a four-game road losing streak and made Maurice a winner in his first trip to Tobacco Road since he was fired by the Hurricanes exactly three years ago.
No coach in Hurricanes history has more victories than Maurice's 268 from 1995 to '03. But he was fired after a slow start to the 2003-'04 season, coached the Maple Leafs' top minor-league affiliate last season and is in his first season as Pat Quinn's replacement.
Ward stopped 21 shots for the Hurricanes.
Carolina trailed 3-1 entering the third period before Williams and Commodore led the Hurricanes' comeback.
Williams pulled Carolina to 3-2 with a power-play goal with 13:57 to play when he lifted a wrist shot from near the goal-line past Raycroft. Commodore tied it about five minutes later when he tapped a rebound from the slot past Raycroft, but Toronto held firm and denied the Hurricanes their third straight home victory.
Sundin had put the Maple Leafs ahead 2-1 midway through the second period when he scored with a 5-on-3 advantage. Darcy Tucker took a rebound of McCabe's shot near the goalmouth and passed down the goal-line to Sundin, who snapped the puck past Ward for his 12th goal of the season.
Minutes later, McCabe also scored on the 5-on-3, blasting a shot from just outside the right circle past Ward to make it 3-1. It was the ninth power-play goal Carolina has allowed during its last three games.
Cole gave Carolina a brief 1-0 lead when he backhanded the puck through Raycroft's legs with four minutes remaining in the first for his 13th goal of the season and fourth goal in his last three home games.
It came seconds after John Pohl misfired on a penalty shot when his wrist shot to the right side was stopped by Ward.
Sundin tied it with about 1:58 left in the period. He zipped through the Carolina defence, took a pass from Kyle Wellwood and fired a wrist shot through Ward's legs.
Notes: Sundin has 858 points with the Maple Leafs and moved ahead of Dave Keon into second place in franchise history in points . . . Hurricanes C Eric Staal has assists in three straight games . . . Carolina captain Rod Brind'Amour (lower body) missed his third straight game . . . New North Carolina State football coach Tom O'Brien was greeted with cheers when he was introduced during a break.