If I remember jQuery correctly, you can extract the target element from the HTML, like the second response on Stackoverflow shows:

$('#submitform').click(function() {
     $.ajax({
     url: "getinfo.asp",
     data: {
         txtsearch: $('#appendedInputButton').val()
     },
     type: "GET",
     dataType : "html",
     success: function (data){
         $('#showresults').html($('#showresults',data).html());
         // similar to $(data).find('#showresults')
     },
});
[download]

For passing in the parameters, either pass them as the data key, or construct an URL-encoded query string and pass that to your call.

Mojolicious may have "too much" for your current taste, but it brings a lot of convenient things to the plate.