To accomplish this, I have tried different approaches: posting WM_PASTE, SendKeys sending ctrl-v... None of the method seems to be working so well.
A friend from work suggested trying WM_COMMAND. Since Spy++ doesn't work with cmd.exe, we had to use brute force to find the correct WPARAM for pasting.
The result is really simple, just one line code with C++:
// hwnd is the window handle of a CMD window
SendMessage(hwnd, WM_COMMAND, 0xfff1, 0);
And here's the C# version with PInvoke:
private static extern IntPtr SendMessage(IntPtr hWnd, uint Msg, IntPtr wParam, IntPtr lParam);
private const uint WM_COMMAND = 0x0111;
SendMessage(hwnd, WM_COMMAND, (IntPtr)0xfff1, IntPtr.Zero);