ServiceProviderControllerActivator.cs

public class ServiceProviderControllerActivator : IHttpControllerActivator
{
    private readonly IHttpControllerActivator _parent;
    private readonly IServiceProvider _provider;

    public ServiceProviderControllerActivator(IHttpControllerActivator parent, IServiceProvider provider)
    {
        _parent = parent;
        _provider = provider;
    }

    public IHttpController Create(HttpRequestMessage request, HttpControllerDescriptor controllerDescriptor, Type controllerType)
    {
        var scope = _provider.CreateScope();
        request.RegisterForDispose(scope);

        var controller = scope.ServiceProvider.GetService(controllerType) as IHttpController;
        if (controller == null && _parent != null)
        {
            controller = _parent.Create(request, controllerDescriptor, controllerType);
        }

        return controller;
    }
}

Startup.cs

public class Startup
{
    public void Configuration(IAppBuilder app)
    {
        var services = new ServiceCollection();
        /* Add Services & Controllers */

        var provider = services.BuildServiceProvider();

        var config = new HttpConfiguration();
        var parentActivator = config.Services.GetService(typeof (IHttpControllerActivator)) as IHttpControllerActivator;
        config.Services.Replace(typeof (IHttpControllerActivator), new ServiceProviderControllerActivator(parentActivator, provider));

        app.UseWebApi(config);
    }
}