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Vine doubled his personal tally just four minutes later with a curling strike that left Williams rooted to the spot.
St Johnstone had a great chance to make it 3-0 just after the half-hour mark when Mehdi Abeid was brought down by Ryan McGivern inside the box. MacLean stepped up, but saw his penalty saved by Williams.
Abeid then had a chance of his own after bursting through the opposition defence, but he could only drag his shot wide.
The Saints finally did get a third just before the hour mark after a good move between MacLean, Murray Davidson and Patrick Cregg saw the latter one-on-one with the keeper, and he duly tucked the effort away.
Hibs pulled a goal back with eight minutes of normal time left when Leigh Griffiths placed his shot past Alan Mannus, but it wasn't enough as St Johnstone ran out comfortable winners.