Insert a div element as parent

You can use replaceChild ^[docs]:

// `element` is the element you want to wrap
var parent = element.parentNode;
var wrapper = document.createElement('div');

// set the wrapper as child (instead of the element)
parent.replaceChild(wrapper, element);
// set element as child of wrapper
wrapper.appendChild(element);

As long as you are not using innerHTML (which destroys and creates elements), references to existing DOM elements are not changed.