The Rockets lost at home for the first time in almost a month, hitting just 35 percent of their shots from the field and turning the ball over 22 times.
Bledsoe scored 20 points in helping lift the Suns back over the breakeven mark following two consecutive losses. Goran Dragic added 19 points for Phoenix and P.J. Tucker had 18.
The Suns built an 11-point halftime lead only to see it cut to two early in the fourth quarter. Phoenix outscored Houston during the final eight minutes 24-17.
Houston produced its lowest number of points for the season with leading scorer James Harden going 3-of-17 from the field while missing all 10 of his tries from 3-point range. He finished with 14 points, one less than Dwight Howard.
The Rockets had won their last six home games and had not lost on their own court since Nov. 9.