Curry fired in six 3-pointers and David Lee contributed a double-double of 20 points and 11 rebounds for the Warriors, who were coming off a Sunday win at Houston.
Golden State had dropped nine of its previous 10 away games prior to its current road trip.
Klay Thompson helped out with 13 points in the victory.
The Hornets could manage only 11 fourth-quarter points in falling for the 11th time in 14 outings.
Ryan Anderson supplied 21 points and nine rebounds for New Orleans.