Derived from https://www.nuget.org/packages/WebPageRouteHandler

WebPagesRouteHandler.cs

// Derived from https://www.nuget.org/packages/WebPageRouteHandler

using System.Web;
using System.Web.Routing;
using System.Web.WebPages;

public class WebPagesRouteHandler : IRouteHandler
{
    readonly string _virtualPath;
    Route _routeVirtualPath;

    public WebPagesRouteHandler(string virtualPath)
    {
        _virtualPath = virtualPath;
    }

    Route RouteVirtualPath =>
        _routeVirtualPath
        ?? (_routeVirtualPath = new Route(_virtualPath.Substring(2), this));

    public IHttpHandler GetHttpHandler(RequestContext requestContext)
    {
        var substitutedVirtualPath = GetSubstitutedVirtualPath(requestContext);
        var index = substitutedVirtualPath.IndexOf('?');
        if (index != -1)
        {
            substitutedVirtualPath = substitutedVirtualPath.Substring(0, index);
        }
        requestContext.HttpContext.Items[ContextExtensions.RouteKey] = requestContext.RouteData.Values;
        return WebPageHttpHandler.CreateFromVirtualPath(substitutedVirtualPath);
    }

    public string GetSubstitutedVirtualPath(RequestContext requestContext)
    {
        var virtualPath = RouteVirtualPath.GetVirtualPath(requestContext, requestContext.RouteData.Values);
        return virtualPath == null ? _virtualPath : "~/" + virtualPath.VirtualPath;
    }
}

public static class RouteCollectionExtension
{
    public static void MapWebPageRoute(this RouteCollection routes, string url, string virtualPath, object defaultValues = null, object constraints = null, string name = null) =>
        routes.Add(name ?? url,
                   new Route(url, new RouteValueDictionary(defaultValues),
                                  new RouteValueDictionary(constraints),
                                  new WebPagesRouteHandler(virtualPath)));
}

public static class ContextExtensions
{
    internal const string RouteKey = "__Route";

    public static string GetRouteValue(this HttpContextBase context, string key) =>
        (context.Items[RouteKey] as RouteValueDictionary)?[key]?.ToString();
}