That's surprising. I took your HTML code and the page doesn't do a full postback. Here is the code
Code:
<%@ Page Language="VB" AutoEventWireup="false" CodeFile="ForumTest.aspx.vb" Inherits="ForumTest" %>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
</head>
<body>
    <form id="form1" runat="server">
    
    <asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<div>
    <asp:UpdatePanel ID="UpdatePanel1" runat="server">
        <ContentTemplate>
            <asp:TextBox ID="txt" runat="server"  Width="20em">
            </asp:TextBox>
            <asp:Label ID="lbl" runat="server">
            </asp:Label>
            <asp:Button ID="btn" runat="server" Text="Click Me!" />
        </ContentTemplate>
    </asp:UpdatePanel>
</div>
    </form>
</body>
</html>
And code behind
Code:
Partial Class ForumTest
    Inherits System.Web.UI.Page

    Protected Sub OnClick(ByVal sender As Object, ByVal e As System.EventArgs) Handles btn.Click
        txt.Text = "Updated time:" + DateTime.Now()
    End Sub
End Class