Edit in JSFiddle

var app = angular.module("app", ['ngRoute']);

app.directive("ngViewLite", ['$route', '$compile', '$controller', function($route, $compile, $controller){
  return {
    terminal: true,
    priority: 400,
    transclude: 'element',
    compile : function(element, attr, linker){
      return function(scope, $element, attr) {
        var currentElement;
                
        scope.$on('$routeChangeSuccess', update); 
        update();
                
        // update view
        function update(){
          var locals = $route.current && $route.current.locals,
              template = locals && locals.$template;

          if(template){
            var newScope = scope.$new();
                        
            linker(newScope, function(clone){
                            
              clone.html(template);
              $element.parent().append(clone);
              
              if(currentElement){
                currentElement.remove();
              }
              
              var link = $compile(clone.contents()),
                  current = $route.current;
                            
              currentElement = clone;
              current.scope = newScope;

              if (current.controller) {
                locals.$scope = newScope;
                var controller = $controller(current.controller, locals);
                clone.data('$ngControllerController', controller);
                clone.children().data('$ngControllerController', controller);
              }

              link(newScope);
              newScope.$emit('$viewContentLoaded');
            });
                        
          }else{
              //cleanup last view            
          }
        }
      }        
    }
  }
}]);


app.controller('RootCtrl', ['$scope', function($scope){
    $scope.title = "Home Page";
}]);

app.controller('CatsCtrl', ['$scope', function($scope){
    $scope.title = "Cats Page";
}]);

app.config(['$routeProvider', function($routeProvider){
    $routeProvider
        .when('/', {
            controller : 'RootCtrl',
            template : '<h1>{{title}}</h1>'
        })
        .when('/cats', {
            controller : 'CatsCtrl',
            template : '<h1>{{title}}</h1>'
        })
        .otherwise({
            redirectTo : '/'
        });
}]);

<div ng-app="app">
    <a href="#/">Home Page</a> | <a href="#/cats">Cats</a>
    <div ng-view-lite></div>
</div>