relay turn off delay

I'm going to be installing a computer into my car.  For the time being, im going to be using an old dell, so a dc-dc powersupply is out.  What I want to do is wire up an inverter so that it will turn off say after 5 or so minutes (or could it be controlled through the 12v line of the computer?).  This would give time for the computer to shut down, but prevent the inverter from draining the battery.

thanks in advance!