put the Search button inside Panel and set DefaultButton property of panel to ID of Search button.
<asp:Panel ID="pnl" runat="server" DefaultButton="btnSearch">
<asp:TextBox ID="txtSearch" runat="server" />
<asp:Button ID="btnSearch" runat="server" Text="Search" />
</asp:Panel>
now when text entered, press Enter. It will cause Default button i.e. btnSearch to be clicked.
Moreover if u dont want to display Search button, set its display to none.
<asp:Button ID="btnSearch" runat="server" Text="Search" style="Display:None;" />
:)