Unable to connect (or authenticate connection) to Google/Gmail on Mackbook Air or iPhone after google password change last week

So the week before last (Starting approximately April 11 or 12 (2015)) - I started getting nearly regular emails from Google to the effect that they had blocked access to my account from an unauthorized device. The locations were where I was, and I wasn't noticing difficulty accessing my accounts - so I kind of ignored it.

I decided (stupidly, it seems) to change my Google password for good measure. Now, I can not connect to Gmail from my mail account (Apple, Mac, Airbook) - nor from my phone (iPhone 6+, native apple mail App).

In settings - when it asks me to enter the password, I do - I get a screen listing the types of info Google wants to manage - (and it implies that it recognizes the password - ) but when I hit 'accept' - I get "Authentication Failed Failed to authenticate with Google" - and from the phone I get a similar but simpler message. I can, however, still log into my google accounts using Safari.

I do not have 2-step authentication turned on, and I tried 'enable access to less secure applications' - neither seem to have changed anything.

(Google) searches not turning up much by way of help yet - but there is another open question on the Apple forums (with no replies) that appears to be describing a similar or identical issue that appears to have started for people in the last few weeks. So far 40 people have indicated they have the same issue as the person reporting the issue - but *no one* has weighed in with an answer or suggestion yet.

I'm running Yosemite 10.10.3, btw. iOS 8.3 (12F70).

Help?