The Hibs striker thundered a 35-yard free-kick off the underside of the bar past the diving Jamie MacDonald, and the ball dropped two feet inside the goal before spinning back for Andy Webster to head over his own bar.
The assistant referee flagged for a corner - much to the frustration of Griffiths, who was booked by referee Euan Norris for complaining about the decision.
John Sutton had an early chance for Hearts when he got in behind the Hibs defence from a MacDonald punt but his shot lacked power and was easily saved by Ben Williams.
Michael Ngoo then had a drive deflected inches wide off the heel of James McPake and from the resulting corner the Hearts striker was unable to get out of the way of Sutton's net-bound header.
Matt Done finally forced MacDonald into action with an under-hit effort from eight yards and the Hearts keeper made a diving save to keep out a Scott Robertson flick from a similar distance at the other side of the box.
But Danny Wilson missed the best chance of the half when he ghosted in at the back post to head a free-kick from Arvydas Novikovas past the post from four yards.
Williams turned the ball round the post after Webster swivelled and hit a volley from the edge of the box but the Hibs keeper was nowhere close to clearing a Brad McKay free-kick shortly after that and had to be rescued by Lewis Stevenson when the ball dropped to Ngoo.
Hearts then had a penalty claim waved away by referee Norris when Hibs defender Alan Maybury tangled with Callum Tapping, but even that would be eclipsed in the late stages by the Griffiths decision.