Target specific widgets by title

widget-title-class.php

<?php
function helper__dynamic_sidebar_params__title_class ( $instance, $widget, $args ) {
	if ( isset( $instance['title'] ) ) {
		$new_class = implode( '_', array( 'widget', $widget->id_base, sanitize_title( $instance['title'] ) ) ) . " ";
		$args['before_widget'] = str_replace( 'class="', 'class="' . $new_class, $args['before_widget'] );

		// For lack of a proper filter, let's just do this ourselves - will have to keep up to date with WP, though. 
		$was_cache_addition_suspended = wp_suspend_cache_addition();
		if ( $widget->is_preview() && ! $was_cache_addition_suspended ) {
			wp_suspend_cache_addition( true );
		}

		$widget->widget( $args, $instance );

		if ( $widget->is_preview() ) {
			wp_suspend_cache_addition( $was_cache_addition_suspended );
		}

		// Return false to prevent display since we just did it
		return false;
	}

	return $instance;
}
add_filter( 'widget_display_callback', 'helper__dynamic_sidebar_params__title_class', 10 , 3 );