I recently wrote an automatic memory leak detector and debugger, which makes this a lot easier (imo) [0]. You write a short input script that drives the UI in some loop, it looks for growing things (objects, arrays, event listener lists, DOM node lists...), and then collects stack traces to find the code that grew them. While it won't find all of the leaks, I was able to eliminate an average of 94% of the live heap growth I observed in 5 web applications (which found new memory leaks in Google Analytics, AngularJS, Google Maps, etc).

More information about the technique can be found in a PLDI paper (which I presented last week :D ), which I tried to write clearly so that it is accessible to a technical audience (i.e., non-academics) [1].

[0] http://bleak-detector.org/

[1] https://dl.acm.org/citation.cfm?doid=3192366.3192376 (shouldn't be paywalled, but if it is, it's also available at [0])