It really would not start WWIII. Who would we fight in this WWIII? North Korea? They don't have enough nuclear weapons to cause any sort of a major war. The kind of thing that the previous post is describing might have happened in the Cold War, but not today.
If Al Qaeda exploded a nuclear weapon in Moscow or Washington, it would be very clear that it had not via a missile. Therefore, there would be no immediate response since it would not be clear who to attack in retaliation.
If you want to create a doomsday scenario, I guess you can say that we would attack North Korea and that China would then attack us. But it's completely far fetched to imagine this.