My application is using SQL Server 2012, EF6, MVC and Web API.
It\'s also using a repository and assorted files such as:
DatabaseFactory.cs
Disposable.c
If you aren't using a repository then I assume you would have some place to write your logic/processing that your service operation would use. I would create a new instance of the Context in that logic/process class method and use its methods directly. Finally, dispose it off right after its use probably under a "using".
The processing method would eventually transform the returned/processed data into a data/message contract which the service returns to the controller.
Keep the data logic completely separate from Controller. Also keep the view model separate from data contract.