Classic film fazed Horowitz badly (3,6,2,2)

I believe the answer is:

the wizard of oz

I'm a little stuck... Click here to teach me more about this clue!

'classic film' is the definition.
'the wizard of oz' can be an answer for 'film' (I've seen this before). I'm not sure about the 'classic' bit.

'fazed horowitz badly' is the wordplay.
'badly' is an anagram indicator (letters in the wrong order).
'fazed'+'horowitz'='fazedhorowitz'
'fazedhorowitz' with letters rearranged gives 'THE WIZARD OF OZ'.

Can you help me to learn more?

(Other definitions for the wizard of oz that I've seen before include "1939 MGM Technicolor movie" , "film" , "He was sought along Yellow Brick Road" .)

I've seen this clue in The Times.

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