Hibs carved out the first decent chance as Griffiths nodded wide a Scott Robertson cross into the box.
Lewis Stevenson was the first player to enter referee Willie Collum’s notebook after 18 minutes for a very late tackle on Paul Dummett down the left side.
From Carey’s resultant free-kick into the box, James McPake headed behind at the expense of a corner.
Hibs midfielder Tom Taiwo capitalised on a defensive blunder by Conor Newton to send a shot on target, but a combination of Craig Samson and Marc McAusland diverted it away from goal.
Saints lived a charmed life at the mid-way point as striker Griffiths rattled Samson’s left hand post with a shot from 14 yards after he left Dummett and Goodwin in his wake down the right hand side.
Hibs, again, pressed for the opener and Jorge Claros left fly with a right foot shot from distance after Robertson picked him out, the effort whistling just wide of Samson’s right hand post.
At the other end, Saints left-back Dummett headed agonisingly wide from a great position at the back post where he connected with Newton’s inviting cross into the danger-zone.
Before half-time there was a great chance to break the deadlock for Saints.
Esmael Goncalves bombed forward on a penetrating run before unleashing a shot at goal but keeper Ben Williams was equal to the task, saving from the Portuguese frontman.
After the break, Done fired a cross towards the back post where Paul Cairney just failed to connect for the visitors, before Saints striker Steven Thompson nodded an effort from the edge of the box straight at Williams.
There was a double substitution by St Mirren manager Danny Lennon at the hour mark with Kenny McLean and Carey leaving the field to be replaced by John McGinn and Lewis Guy.
As a result, Saints adopted a 4-3-3 formation as they sought make that crucial breakthrough in front of goal.
Griffiths continued his tricks and turns whenever he was in possession inside the penalty box but Goodwin was able to keep a good eye on the Hibs number nine and stand up to his threat well.
Centre-back McAusland was the next player cautioned after 66 minutes for a foul on Taiwo but from the free-kick Saints keeper Samson was well placed to take Griffiths’ shot.
Hibs, though, won a penalty kick in quite controversial circumstances with 18 minutes remaining when Goodwin was adjudged to have pushed Done in the box as they challenged for possession from Taiwo’s pass on the right hand side.
Up stepped Griffiths to send Samson the wrong way from the spot for 1-0.
With 11 minutes remaining, Griffiths stung the fingers of Samson with a powerful angled effort after he picked up a David Wotherspoon pass but there was no-one in front of goal for Hibs to tuck the rebound away. Thompson, for Saints, saw a backward header from McGinn’s cross taken by Williams as they sought a leveller, but failed.