[SalesForce] Getting OAuth 2.0 Refresh Token returns invalid_client_id

My Connected App settings are the following:

(1) Setup->Manage Apps->Connected Apps->FirstConnectedApp->Refresh Token Policy: "Refresh token is valid until revoked"

(2) Setup->Security Controls->Session Settings->Session Timeout->Timeout Value: "15 minutes".

I can obtain a new access token (using Web Server Flow) and use it to update data using Salesforce Connected App.

Now, I go home and come back the next day to update some data using HTTPS and PATCH, and I get the following response:

[
    {
        "message": "Session expired or invalid",
        "errorCode": "INVALID_SESSION_ID"
    }
]

This error makes perfect sense because the session has expired. Now, I attempt to follow the "Understanding the OAuth Refresh Token Process" (https://developer.salesforce.com/docs/atlas.en-us.api_rest.meta/api_rest/intro_understanding_refresh_token_oauth.htm). I send a HTTPS POST using the following settings:

• Header item: "Content-Type: x-www-form-urlencoded"
• Header item:
  "Authorization: client_id:'Client ID/Consumer Key',
  client_secret:'Client Secret/Consumer Secret'"
• Body item:
  "grant_type=refresh_token&refresh_token='refresh_token'"

Now, I submit this HTTPS POST and I get the following response:

{
    "error": "invalid_client_id",
    "error_description": "client identifier invalid"
}

Why would I be getting this response?

I double checked to make sure that in fact the "Client ID" matches the "Consumer Key" in my Connected App.