I was getting this error too and the reason ended up being wrong call url. I am leaving this answer here, if someone else happens to mix the urls and getting this error. Took me hours to realize I had wrong URL.
Error I got (HTTP code 400):
{
"error": "unsupported_grant_type",
"error_description": "grant type not supported"
}
I was calling:
https://MY_INSTANCE.lightning.force.com
While the correct URL would have been: