Index: src/wp-admin/css/customize-controls.css
===================================================================
--- src/wp-admin/css/customize-controls.css	(revision 29275)
+++ src/wp-admin/css/customize-controls.css	(working copy)
@@ -145,6 +145,32 @@
 	content: "\f141";
 }
 
+.control-section.control-panel > .accordion-section-title {
+	padding-left: 45px;
+}
+
+.control-section.control-panel > .accordion-section-title:before {
+	font: normal 20px/1 dashicons;
+	position: absolute;
+	top: 11px;
+	left: 14px;
+	-webkit-font-smoothing: antialiased;
+	-moz-osx-font-smoothing: grayscale;
+}
+
+/* Don't override custom icons, which get an additional class. */
+.control-section.control-panel > [class="accordion-section-title "]:before {
+	content: "\f111";
+}
+
+#accordion-panel-widgets > .accordion-section-title:before {
+	content: "\f116";
+}
+
+#accordion-panel-menus > .accordion-section-title:before {
+	content: "\f333";
+}
+
 .accordion-sub-container.control-panel-content {
 	display: none;
 	position: absolute;
Index: src/wp-includes/class-wp-customize-section.php
===================================================================
--- src/wp-includes/class-wp-customize-section.php	(revision 29275)
+++ src/wp-includes/class-wp-customize-section.php	(working copy)
@@ -215,6 +215,15 @@
 	 */
 	public $sections;
 
+ 	/**
+	 * Icon for the panel to show in UI.
+	 *
+	 * @since 4.0.0
+	 * @access public
+	 * @var string
+	 */
+	public $icon = '';
+
 	/**
 	 * Constructor.
 	 *
@@ -243,8 +252,8 @@
 	 */
 	protected function render() {
 		?>
-		<li id="accordion-section-<?php echo esc_attr( $this->id ); ?>" class="control-section control-panel accordion-section">
-			<h3 class="accordion-section-title" tabindex="0">
+		<li id="accordion-panel-<?php echo esc_attr( $this->id ); ?>" class="control-section control-panel accordion-section">
+			<h3 class="accordion-section-title <?php echo esc_attr( $this->icon ); ?>" tabindex="0">
 				<?php echo esc_html( $this->title ); ?>
 				<span class="screen-reader-text"><?php _e( 'Press return or enter to open panel' ); ?></span>
 			</h3>