You can try with the protocol data:text/attachment
Like in:
<html>
<head>
<style>
</style>
</head>
<body>
<div id="hello">
<span>world</span>
</div>
<script>
(function(){
document.location =
'data:text/attachment;,' + //here is the trick
document.getElementById('hello').innerHTML;
//document.documentElement.innerHTML; //To Download Entire Html Source
})();
</script>
</body>
</html>
Edit after shesek comment