A remarkable blunder by Buddies goalkeeper Craig Samson after six minutes gifted Griffiths his first Hibees' goal since signing on loan from Wolves in the summer, but his blushes appeared to have been spared when a Paul McGowan double within two minutes put the home side in front.
However, Hibs defender Sean O'Hanlon levelled with a header in the 37th minute before Griffiths fired the Leith men back in front with an angled drive and with no more scoring after the break the points went back east.
In his programme notes Buddies boss Danny Lennon claimed that "long ball, kick and rush football over the years has dragged our game down a peg or two" while insisting a "revolution" was required.
Revolution was perhaps not the word he searched for in the sixth minute as Samson handed Griffiths the opening goal on a plate.
There was no obvious danger when the Buddies goalkeeper took a Lee Mair pass-back to his feet and most people inside the ground expected him to kick it long.
However, for some inexplicable reason he hesitated then tried to go past the Hibs striker who easily robbed him and knocked the ball into the empty net.
It took some time for St Mirren to recover but they eventually began to threaten and in the 25th minute midfielder Kenny McLean had a right-footed effort from 20 yards which was easily saved by Graham Stack.
There was still some surprise though when McGowan scored twice in two minutes to turn the game on its head.
In the 32nd minute a spell of home pressure ended with right-back David van Zanten's cross being headed powerfully home by McGowan past Stack.
Then, from Gary Teale's looping free-kick to the back post, the ball broke to the edge of the box after Steven Thompson's header was blocked and McGowan rifled it in low.
But the scoring had not stopped there and in the 37th minute when David Wotherspoon sent a long free-kick to the back post, O'Hanlon rose highest to head back across Samson and in.
There was more drama in the 41st minute when Hibs striker Garry O'Connor set up Griffiths who fired in an angled drive past Samson to reclaim the lead for the visitors.
Nigel Hasselbaink replaced midfielder Steven Thomson in the 52nd minute to partner Thompson in attack and that change seemed to energise the home side although in their desire to get back level they were taking chances at the back.
But both sides had tightened up and the play became constrained within the middle of the park and the offside flag being raised at both ends.
Thompson took a pass from McGowan and brushed past Hibs defender Richie Towell inside the box but his shot was saved by Stack and when the ball fell to Hasselbaink just eight yards out he appeared to mis-hit his effort past the post, albeit under some pressure from the Hibs defenders.
Hibs should have sealed the win in the 79th minute but substitute Akpo Sodje missed the target from under the bar when he was set up perfectly by fellow sub Lewis Stevenson.
The visitors soon found themselves under pressure again and after Hasselbaink cut the ball across the box, McLean had a shot blocked before Jim Goodwin came close seconds later with a drive.
As the pressure intensified, Stack denied Thompson with a reflex save from point-blank range and the Easter Road side survived the corner and despite some more close calls they held on for the three points.