Michael Beasley had 15 points, Markieff Morris added 14, Shannon Brown scored 12 and Luis Scola finished with 11 for the Suns, who have won three of their past four, including both home contests.
Tyler Honeycutt scored 17 points and Jason Thompson added 14 for the Kings, who had won two straight.
The Suns rallied from a slow start and early 12-point deficit to take a 50-44 lead at halftime and quickly extended their advantage. Dudley hit a 3-pointer and completed a three-point play in the first 90 seconds of the third quarter to give Phoenix a 58-44 lead.
Beasley added four straight points on a 7-foot jumper and a dunk to give Phoenix a 76-60 with 2:24 left in the period.
Sacramento whittled the lead to 81-75 on a layup by Thomas Robinson with 7:54 remaining. But Morris hit a 20-footer and a dunk, and Dudley scored 11 points in the game's final 3:07 as the Suns opened their biggest lead, 103-85, before settling for the 15-point win.
Featuring what, barring injury or other surprises, will be the season-opening starting lineup, the Suns got off to a sloppy start. In the game's first four minutes, Phoenix committed seven turnovers, missed three shots and fell behind 12-2.
But the Suns started to work themselves back into the game and took the lead for good on a 16-foot jump shot by Dudley with 46 seconds left in the first half.