The Match Regular Expression node does have a multiline parameter to account for that; when set to True, the ^ and $ anchors no longer match line endings and the . wildcard will also match \r and \n. But more importantly, you should rarely, if ever, write a regex that uses that . wildcard. You might parallel it to global variables in LV - there are valid use cases, but they are far and few. Using more specific matching makes debugging and readability much more straightforward.
Though my solution does have a flaw - if there's a nested > (within an attribute, for example), the regex will break. This way why regular expressions are almost never the correct solution for HTML/XML/*ML problems, it's a job for a proper parser (TidyHTML, for example).