Half-time substitute Griffiths wasted no time finding the equaliser, firing in off the post from a tight angle.
Stack then made two saves to deny James Dayton in a lively second half.
Billy Brown's bid to become Hibernian manager on a permanent basis appeared to be on the rocks at the interval after an insipid showing.
The home side were chasing shadows for long spells as Kilmarnock knocked the ball around confidently.
Former Hibs midfielder Dean Shiels was first to threaten, weaving his way into the left of the penalty area and cutting onto his right foot but Stack held the shot at his near post.
The opening goal came as Hibs failed to clear a corner. Stack could only push away a stinging half-volley from Buijs and Pascali tapped in the follow-up.
With striker Garry O'Connor isolated up front, Hibs posed no threat in the final third of the park until Brown altered his team at the break.
Griffiths came on for Danny Galbraith, with Richie Towell replacing Michael Hart, while Killie replaced striker Paul Heffernan with Gary Harkins.
Griffiths, who had been ill during the week, joined O'Connor up front and the on-loan Wolves striker's impact was swift as he equalised five minutes after being introduced following a strong run by Ivan Sproule.
Goalkeeper Anssi Jaakkola palmed away Sproule's attempted cross and Griffiths collected on the left before netting off the post from an acute angle.
Griffiths then prodded wide after surging into the right side of the box before O'Connor shot tamely from 30 yards.
Stack saved a Shiels effort at his near post and Liam Kelly drove wide from long range as Kilmarnock rediscovered some of their earlier passing rhythm.
Substitute Dayton's header lacked the pace to trouble Stack before Shiels chipped onto the top of the Hibs net with an audacious effort.
shot on the turn
was hit straight
at Stack as the
Special mention to debut teenager Matthew Kennedy, (pictures right) who replace Hooky after 77 mins.