Use of comma

I have been given the following section, and I need to correct the grammatical errors.

On his deathbed the minister was entreated to remove his veil and clear his name of the dark mystery surrounding his otherwise upright and holy life.

My revision:

On his deathbed, the minister was entreated to remove his veil and clear his name of the dark mystery surrounding his otherwise upright and holy life.

Should the comma after "deathbed" not be placed, given that the introductory adverb prepositional phrase "On his deathbed" is very short (3 words)