The 'Video Games' singer sang a surprise version of the band's 1993 track, written by Kurt Cobain, at the Enmore Theatre in Sydney, Australia.
The Sydney Morning Herald review of the show said that Del Rey's "awkward vulnerability [combined] well with Kurt Cobain's seething rage" during the cover, but other online comments described her as "having no stage presence".
One particularly disappointed user said: "I'm a long time Nirvana fan also and no-one should attempt to do it as it can't be done better by anyone else!"
Del Rey recently announced plans to re-release her debut Born To Die with seven new tracks.
Watch Lana Del Rey cover 'Heart Shaped Box' below: