Brown scored 14 of his 22 points in the big frame, during which the Suns outscored the Kings 31-14 and pulled away for their straight triumph following a seven-game skid.
Dudley added 20 points while Marcin Gortat chipped in with 14, 13 rebounds and six blocked shots in the Suns' victory.
Luis Scola contributed a double-double of 14 points and 10 assists for Phoenix.
Jimmer Fredette came off the bench for 22 points while DeMarcus added nine and 10 rebounds for Sacramento.
2014: The Year in Music [PHOTOS]