David's helpful answer provides the crucial pointers and helpful links.
To put them to use in a self-contained example that implements the sample scenario in the question, using the Windows API via P/Invoke (System.Windows.Forms is not involved):    
using System;
using System.Runtime.InteropServices; // For the P/Invoke signatures.
public static class PositionWindowDemo
{
    // P/Invoke declarations.
    [DllImport("user32.dll", SetLastError = true)]
    static extern IntPtr FindWindow(string lpClassName, string lpWindowName);
    [DllImport("user32.dll", SetLastError = true)]
    static extern bool SetWindowPos(IntPtr hWnd, IntPtr hWndInsertAfter, int X, int Y, int cx, int cy, uint uFlags);
    const uint SWP_NOSIZE = 0x0001;
    const uint SWP_NOZORDER = 0x0004;
    public static void Main()
    {
        // Find (the first-in-Z-order) Notepad window.
        IntPtr hWnd = FindWindow("Notepad", null);
        // If found, position it.
        if (hWnd != IntPtr.Zero)
        {
            // Move the window to (0,0) without changing its size or position
            // in the Z order.
            SetWindowPos(hWnd, IntPtr.Zero, 0, 0, 0, 0, SWP_NOSIZE | SWP_NOZORDER);
        }
    }
}