I have seen this before with D-Link.
The reason for the Zener to explode is that it's just doing what it was put there for. Protect the router in case of too high input-voltage from the mains adapter. And this is where the REAL problem is. In many switched-mode adapters (the ones without an old fashion heavy transformer with an iron-core) electrolytic cap's go bad. That will happen in MANY, MANY of these adapters. The ASUS WL-500g router adapter is a good example and so are a lot of adapters for DVB-T receivers.
Take the adapter apart (if glued, put in a wise and apply some brute force and try to pry open with a flat screwdriver) and replace all big & small electrolytic caps. But first you check if the switching transistor (may be an Integrated Circuit) or any diode is shorted. In that case buying a new adapter is in order.
Now replace the dead zener inside the router (6,8V/1Watt in my opinion) and you're set to go.
Good luck,
/tri-comp