The win followed Thursday's disappointing 3-2 loss to the Washington Capitals when Carolina yielded two goals in the final three minutes.
Carolina defenseman Dennis Seidenberg created the tie at 11:06 following a pass from Corvo.
Netminder Michael Leighton was credited with 22 saves on 23 shots for the Hurricanes, winners in three of the last four contests.
Carolina's Peter Laviolette became the winningest American-born coach in NHL history.
Center Mike Fisher gave Ottawa its 1-0 lead at 18:08 of the second period, and that lead stood up before Curvo scored.
Goalie Martin Gerber was beaten twice on 30 shots for the Senators, who had won two in a row.
2014: The Year in Music [PHOTOS]