Nash hit 13-of-16 from the floor and helped the Suns put together a game-ending 25-9 run after the Hornets had closed within a single point early in the fourth quarter.
Nash had 10 assists, giving him 6,521 for his career. Kevin Johnson had held the team's career record with 6,518.
Marcin Gortat added 23 points and 11 rebounds for the Suns, delivering his 12th double-double in the last 13 games.
New Orleans lost its third in a row and has dropped 12 out of 13. Greivis Vasquez scored 20 points and dealt out 12 assists for the Hornets, both career highs.