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You're doing it almost right. Use homogeneous coordinates and it should work - at least it works for me.

Point3d p1(x1, y1, 1);
Point3d p2 = Point3d(Mat(H*Mat(p1))); //this is a complicated way to do: H*p1 - perhaps it can be done in a simpler way?
p2 /= p2.z; //normalize the output to get the right (x2, y2, 1)