The Suns led by 25 points in the third quarter, but the Wizards cut it all the way down to three after John Wall scored eight straight points, the last four on a dunk after dribbling the length of the court and an easy layup with no resistance from the Phoenix defense with 90 seconds left.
But Bledsoe knocked down a long 3-pointer at the other end and Wall missed a three for the Wizards, ending the rally.
Gerald Green had 18 points off the bench for the Suns, who have won seven of their last eight, including five in a row for the third time this season.
Wall scored 29 and Marcin Gortat added 17 points for the Wizards, who have lost four of five.
Wizards guard Bradley Beal left the game late in the second quarter with a right hip pointer after going to the floor under the basket but returned in the third and had eight points.
The Suns snapped a three-game losing streak to Washington.
Phoenix heated up late in the second quarter for a 10-point lead at halftime and scored 17 of the first 21 points in the third quarter to take a 23-point lead.
It reached 25 on a Markieff Morris jumper that made it 75-50 with 5 1/2 minutes left in the third. But the Wizards countered with a 17-2 run, capped by Wall's back-to-back 3-pointers.
That helped trim the lead to 10 entering the fourth quarter.
Earlier, the Suns led 25-23 after the first quarter and 54-44 at halftime behind a 12-1 run led by Dragic's five points. They shot 55 percent in the half and Dragic had 14 points.