You can set ref for child components then in parent can call via $refs:
Add ref to child component:
<my-component ref="childref"></my-component>
Add click event to parent:
<button id="external-button" @click="$refs.childref.increaseCount()">External Button</button>
var vm = new Vue({_x000D_
el: '#app',_x000D_
components: {_x000D_
'my-component': { _x000D_
template: '#my-template',_x000D_
data: function() {_x000D_
return {_x000D_
count: 1,_x000D_
};_x000D_
},_x000D_
methods: {_x000D_
increaseCount: function() {_x000D_
this.count++;_x000D_
}_x000D_
}_x000D_
},_x000D_
}_x000D_
});
_x000D_
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.js"></script>_x000D_
<div id="app">_x000D_
_x000D_
<my-component ref="childref"></my-component>_x000D_
<button id="external-button" @click="$refs.childref.increaseCount()">External Button</button>_x000D_
</div>_x000D_
_x000D_
<template id="my-template">_x000D_
<div style="border: 1px solid; padding: 2px;" ref="childref">_x000D_
<p>A counter: {{ count }}</p>_x000D_
<button @click="increaseCount">Internal Button</button>_x000D_
</div>_x000D_
</template>
_x000D_