One way would be to unset your Blog page at Settings > Reading, de-select it as your posts page. Then go to Pages > Blog and click the Page Builder plugin tab and insert a Post Loop widget. That would free you up to select a page template in the right column drop down menu. Assuming all other pages use Full Width you could use Default, thereby showing the sidebar.
Another way would be to use the Jetpack plugin’s module: Widget Visibility: http://jetpack.me/support/widget-visibility/. You can specify when a widget should or shouldn’t be displayed.