The Suns, who came in with a one-game lead over the Memphis Grizzlies for the eighth and final seed in the Western Conference, scored the game's final seven points to avoid a sour start to a critical three-game road trip.
Gerald Green made four 3-pointers and logged a game-high 21 points for Phoenix, which has surged down the stretch with nine wins over its last 11 games. Goran Dragic totaled 20 points and nine assists and Bledsoe checked in with 16 points, six assists and six rebounds.
Anthony Davis did not play in New Orleans' sixth straight loss due to back spasms. Jeff Withey played more minutes in his absence and led the club with 17 points. Darius Miller and Anthony Morrow each netted 14 in the setback.
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