WOO HOO!
After an incredibly frustrating day/night dealing with this issue the solution presented by Eric Root worked. I updated to 10.10.4 via the app store and then started having the issue outlined above. I could not browse the web in Chrome or Safari for more than a few minutes before pages would stop loading, but I did still have an internet connection as streaming music services still worked, etc. I tried many different solutions, I even did a virus scan for the first time on my MacBook Pro since owning an Apple device, which by the way found no issues. Nonetheless nothing worked until I woke up this morning and installed the combo update. Now I am back in business. So frustrating that such an annoying issue originated from an Apple update, but I guess no one/company is perfect... 😉
On a different note. Has anyone noticed after applying the 10.10.4 update that their recovery partition still says "Recovery 10.10.3"? Is there a fix for this? I launched it and it still works as far as I can tell. I can access help online, Disk Utility, Fresh Install, etc.