Craft 3 Plugins - Setting Template Path To Site Templates
Ok I've made sense of this - if you set the view template mode/context to site, then use the view renderTemplate() method (not render) it works.

So this is how you achieve the same thing in Craft 3. 

# Set the template context to the site mode.
Craft::$app-&gt;getView()-&gt;setTemplateMode(View::TEMPLATE_MODE_SITE);

# Now using the renderTemplate() method, it will work.
$html = Craft::$app-&gt;getView()-&gt;renderTemplate("/path/to/particular/site/template");


Edit: Lenka commented pointing out there is actually some official documentation on this.