Kevin Moon kicked off the rout for St Johnstone with a deflected shot on 45 minutes after Saints had missed several first-half chances at McDiarmid Park.
Paul Sheerin scored two penalties in three minutes before Leigh Griffiths countered for Livingston in 63 minutes.
Steven Milne slotted Saints' fourth a minute later before Livi's Murray Davidson turned in a near-post corner.
Milne completed the scoring a minute later, in 81 minutes, when he finished from a tight angle.
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