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.
Notable deaths of 2014 [PHOTOS]