Assuming you are using jQuery, instead of using $.get or $.getJson, use the more generic $.ajax and explicitly set the cache value to false. The following is an example:
$.ajax({
url: "/Controller/Action",
cache: false,
type: "GET",
dataType: "json",
success: function(data, textStatus) {
alert("success");
}
});
A little more code required (not much though) than using .getJson or .get but will solve the problem cleanly without appending random numbers.