How to use Jeditable plugin with admin-ajax.php?

Here is another way:

$('.editable').editable(function(value, settings) { 

 $.post(
    ajaxurl,
    { action: 'ajax_action',
              data: data,
              moreData: moreData
    }, function(response) 
               {

           });

      return(value);
 }, 

 { 
   submit: 'Ok',
   tooltip: 'Click to edit title',
   cancel    : 'Cancel',
   event     : "dblclick"
 });

where value is what has been inserted in the editable field.