Dragic scored 13 of his 18 points down the stretch and Markieff Morris added 14 as the Suns broke a two-game losing streak.
Michael Beasley also reached double figures with 10 points while P.J. Tucker and Hamed Haddadi dominated the glass with a combined 22 rebounds.
James Harden poured in 38 points but it wasn't enough for the Rockets, who dropped their second in three games.
Carlos Delfino put in 21 points for Houston.