After a few hours coding, I can say that I have succesffully written the code to patch credentials for a SQL Azure dataset in PowerBI.com running in DirectQuery mode. I have posted a simple C# console application to use as a reference project at https://github.com/CriticalPathTraining/PbixInstallerForPowerBI.
You can see all the code required in a single C# file at here.
First, you need to retrieve the Gateway ID and the Datasource ID for the target dataset to be updated.
After that, you use the gateway id and the datasource ID to execute a HTTP PATCH operation to update the credentials.
After that, bob's your unkle and the DirectQuery report is able to connect to the SQL Azure database. For me, the confusing part is that you must reference a gateway ID even though there isn't really a Power BI gateway invovled such as a personal gateway or the On-premises gateway. I guess it's a conceptual gateway. It's also a bit ironic that it doesn't work yet if an actual gateway is involved 
The unfortunate part about this is that there is a handy .NET API that wraps all these Power BI REST calls and makes it much easier to code. But this API only works for Power BI Embedded and not for PowerBI.com even though the underlying REST calls between PowerBI.com and Power BI Embedded are almost identical. My guess is that Microsoft needed to get this API out the door in a hurry to give customers traction in getting started with Power BI Embedded. Hopefully, this Power BI .NET API will be modified in the future to use PowerBI.com workspaces in additon to Power BI Embedded worksspces. Until then we will have to write our code just as I have in the PbixInstallerForPowerBI reference application.