Remember - partial view stayed on server.
so look into retrieving action result using ajax.
<div id="container">
@Html.Partial("_IndexPartial")
</div>
@Ajax.ActionLink("Change data", "Index", "Home", new {}, new AjaxOptions{UpdateTargetId = "container"}, new {someparam = "somevalue"})
http://msdn.microsoft.com/en-us/library/system.web.mvc.ajax.ajaxextensions.actionlink(v=vs.108).aspx[
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You can also look into loading json packet through web api and render it on client using template (if you are using knockout, kendo, jquery-templates or similar library) etc.
In fact goal can be achieved in number of ways - up to you.