A small hint is when ping bitdivine.com fails, even though dig bitdivine.com succeeds and Chrome, which uses it's own DNS server rather than the system one, is fine. It seems that apple has changed their DNS client from mDNSResponder to discoveryd and the latter is having some teething problems.
This worked for me:
Add Google's name servers to those listed in the system preferences (under System Preferences->Networking->Wifi->Advanced->DNS):
Restart discoveryd by running this in Terminal:
sudo launchctl unload -w /System/Library/LaunchDaemons/com.apple.discoveryd.plist sudo launchctl load -w /System/Library/LaunchDaemons/com.apple.discoveryd.plist
There might well be a better way. It depends on what you trust.