Dany Heatley and Anton Volchenkov also scored and Jason Spezza had an empty-net goal and two assists for the Senators, who scored three third-period goals to win their seventh in eight games.
Ottawa's game-winner came on an efficient sequence which started when the Senators brought the puck up on a late rush, working it to Spezza. He skated toward the goal-line from the right side and drew goalie John Grahame toward him before firing a last-second pass to Redden, who snapped the puck into an open net.
Eric Staal and Josef Vasicek scored 19 seconds apart in the second period and Cory Stillman added two assists for the Hurricanes, who had a two-game winning streak ended and fell to 23-2 when leading after two periods.
Ottawa's Martin Gerber, supplanted by Cam Ward as the Hurricanes' starter during last year's playoffs, stopped 23 shots against his former team. Grahame, now Ward's backup, made 31 saves in his third straight start.
Volchenkov tied it with just over nine minutes left in regulation with his first goal of the season. He took a cross-ice pass at the right point from Chris Phillips and rocketed a slap shot past Grahame to make it 2-2.
The Hurricanes fell behind 1-0 in the second period before taking the lead with two quick goals.
Stillman had the puck in the right circle and froze the Ottawa defence by briefly glancing toward the net, then fired a quick pass to Staal, who snapped the puck past Gerber with 9:45 left. Seconds later, Vasicek stuffed the rebound of a long slap shot through Gerber's legs for his first goal since rejoining the Hurricanes on Feb. 9.
Staal scored for just the third time in 14 games and 26th of the season, and his goal was Carolina's first on the power play in four games. They entered 0-for-11 with the man advantage during their previous three games.
Heatley gave Ottawa a 1-0 lead with his team-leading 37th goal early in the second, tapping a rebound past Grahame for his fifth goal in four games.
Notes: Heatley and Spezza each extended their point streaks to eight games. . . . RW Anson Carter made his home debut for the Hurricanes. He was acquired last week from Columbus for a draft pick, and skated on a line with Staal and LW Ray Whitney.