Access router outlet component from parent

Make use of activate event for the same . Whenever we load a component in router outlet a activate event is emitted make use of that to get the component ref and call the respective method.

Parent Component

  <div class="container">
    <router-outlet (activate)="onActivate($event)"></router-outlet>
  </div>

Template

  onActivate(componentRef){
    componentRef.works();
  }

Child Comp

 works(){
    console.log("works");
  }

A small addition to @Rahul Singh great answer:

Make sure you check, which component instance is returned in the
(staying at Rahul's example) onActivate(componentRef) method,
and only call works(), if that component indeed has such method.

Example:

     onActivate(componentRef){
       if(componentRef instanceof ChildWithWorksMethodComponent){
         componentRef.works();
         return;
         }
         console.log("This is not the ChildWithWorksMethodComponent");
      }  

Otherwise, every time you navigate to a route, which component doesn't have such method, your console log will be full of errors like:

ERROR TypeError: componentRef.works is not a function

Router-outlet is related to routing it has nothing to do with accessing the child component methods.You have to use @ViewChild for accessing child component functions from the parent.You can find the example here

update

If above isn't a feasible solution in your case,you may tap into activate event to get reference of instantiated component inside the router outlet.

From the docs

A router outlet will emit an activate event any time a new component is being instantiated, and a deactivate event when it is being destroyed.

Hence you can use these feature and get your work done.You can see elaborated answer here and a plunker is attached in the same answer