Washington improved to 8-9 after losing five of its previous six games.
The teams combined for 46 turnovers.
The Wizards took a 104-103 lead on Otto Porter‘s three-point play with 1:42 to play. Beal hit a floater with 47.9 seconds to play for a 106-103 lead, Bledsoe made a layup with 15.9 left, and Beal added two free throws with 11.6 left for a 108-105 advantage.
Knight attempted a 3-pointer with 8.8 left, but Beal fouled him. Knight missed two of the three, with Beal also missing a free throw after Phoenix was called for a technical foul.
Garrett Temple made one of two free throws for Washington with 6.3 seconds to play, and Bledsoe missed a 3-pointer as time expired.
Phoenix, which lost an 18-point lead in a loss at Detroit on Wednesday night, led by 10 early in the fourth quarter.
Suns: Center Tyson Chandler missed his fourth straight game because of a strained right hamstring. Coach Jeff Hornacek said that he hoped Chandler would return within the next few games. Markieff Morris returned after missing the Detroit game with a bruised left knee.