The Rockets came back from a 54-45 halftime deficit and rookie Chase Budinger's tie-breaking 3-pointer gave them a 76-73 advantage with 8:30 left in the fourth period.
Oklahoma City tied it once, but did not lead in the late stages.
Trevor Ariza scored 17 with three assists and four steals and David Andersen 12 with eight rebounds. Brooks added four assists and five steals, while Landry had 10 rebounds for the Rockets, who broke a two-game skid.
Kevin Durant's 25 points, nine rebounds and six assists led Oklahoma City.
Russell Westbrook scored 20 points with five assists, and Jeff Green added 12 points and seven rebounds for the Thunder, who had won two straight.