diff --git a/packages/block-library/src/embed/wp-embed-preview.js b/packages/block-library/src/embed/wp-embed-preview.js
index ccfb0449819b8..4b2c271c3c943 100644
--- a/packages/block-library/src/embed/wp-embed-preview.js
+++ b/packages/block-library/src/embed/wp-embed-preview.js
@@ -4,11 +4,13 @@
 import { Component, createRef } from '@wordpress/element';
 import { withGlobalEvents } from '@wordpress/compose';
 
+/** @typedef {import('@wordpress/element').WPSyntheticEvent} WPSyntheticEvent */
+
 /**
  * Browser dependencies
  */
 
-const { FocusEvent } = window;
+const { FocusEvent, DOMParser } = window;
 
 class WpEmbedPreview extends Component {
 	constructor() {
@@ -18,6 +20,43 @@ class WpEmbedPreview extends Component {
 		this.node = createRef();
 	}
 
+	componentDidMount() {
+		window.addEventListener( 'message', this.resizeWPembeds );
+	}
+
+	componentWillUnmount() {
+		window.removeEventListener( 'message', this.resizeWPembeds );
+	}
+
+	/**
+	 * Checks for WordPress embed events signaling the height change when iframe
+	 * content loads or iframe's window is resized.  The event is sent from
+	 * WordPress core via the window.postMessage API.
+	 *
+	 * References:
+	 * window.postMessage: https://developer.mozilla.org/en-US/docs/Web/API/Window/postMessage
+	 * WordPress core embed-template on load: https://github.com/WordPress/WordPress/blob/master/wp-includes/js/wp-embed-template.js#L143
+	 * WordPress core embed-template on resize: https://github.com/WordPress/WordPress/blob/master/wp-includes/js/wp-embed-template.js#L187
+	 *
+	 * @param {WPSyntheticEvent} event Message event.
+	 */
+	resizeWPembeds( { data: { secret, message, value } = {} } ) {
+		if (
+			[ secret, message, value ].some( ( attribute ) => ! attribute ) ||
+			message !== 'height'
+		) {
+			return;
+		}
+
+		document
+			.querySelectorAll( `iframe[data-secret="${ secret }"` )
+			.forEach( ( iframe ) => {
+				if ( +iframe.height !== value ) {
+					iframe.height = value;
+				}
+			} );
+	}
+
 	/**
 	 * Checks whether the wp embed iframe is the activeElement,
 	 * if it is dispatch a focus event.
@@ -38,11 +77,17 @@ class WpEmbedPreview extends Component {
 
 	render() {
 		const { html } = this.props;
+		const doc = new DOMParser().parseFromString( html, 'text/html' );
+		const iframe = doc.querySelector( 'iframe' );
+		if ( iframe ) iframe.removeAttribute( 'style' );
+		const blockQuote = doc.querySelector( 'blockquote' );
+		if ( blockQuote ) blockQuote.style.display = 'none';
+
 		return (
 			<div
 				ref={ this.node }
 				className="wp-block-embed__wrapper"
-				dangerouslySetInnerHTML={ { __html: html } }
+				dangerouslySetInnerHTML={ { __html: doc.body.innerHTML } }
 			/>
 		);
 	}