Motherwell striker Michael Higdon missed from the spot in between the second-half double after David Wotherspoon's impressive long-range strike had put the visitors in front.
Danny Handling completed what looks like a thrashing on paper but Motherwell will still feel aggrieved at the performance of referee Stevie O'Reilly, who did not finish the game.
The fixture has seen plenty of drama in recent seasons - a four-goal comeback from the hosts completed in injury-time, a penalty shootout, a floodlight fire that sparked an abandonment and a total of 30 goals in five games.
This encounter had a phantom goal and three controversial penalties in 10 minutes were added to the list. O'Reilly and assistant Francis Andrews failed to spot Stevie Hammell's header bouncing clearly over the line before Hibernian goalkeeper Ben Williams scooped it out of his goal.
The blunder denied Motherwell an equaliser and O'Reilly had another huge say on proceedings in the second half when he penalised Darren Randolph for a challenge on Griffiths despite the home goalkeeper getting a strong hand to the ball.
O'Reilly then awarded two more disputed penalties before being replaced by Iain Brines, although he did not appear to be limping.
The game was action-packed from the start. Jamie Murphy had an effort saved by Williams after five minutes before Wotherspoon's backheel flick spun just wide.
Griffiths then drove wide from 20 yards and James McPake cleared Humphrey's cross from his goalmouth after Higdon and Keith Lasley both passed up brief glimpses of goal.
Hibernian took the lead in the 28th minute. Paul Crainey turned Fraser Kerr and slipped the ball to Wotherspoon, who took a touch and fired into the top corner from 22 yards.
Motherwell thought they had equalised six minutes later when Humphrey knocked the ball past Ryan McGivern and sent over a powerful cross that was met by Hammell at the back post. The left-back headed the ball down and on target only for Williams to claw it out.
The ball looked over the line from distance and television replays confirmed there was no doubt about it, but O'Reilly and assistant Francis Andrews played on.
Motherwell continued the pressure before the break. Humphrey beat Williams to a long ball but the ball ran away from him, Higdon was too high from 12 yards as he stretched to meet Henrik Ojamaa's cross first time and the Estonian then shot just wide following a counter-attack although he was penalised for what appeared to be a collision with Jorge Claros.
The end-to-end action continued after the break. Griffiths twice threatened and Humphrey and Nicky Law came close from distance at the other end. Higdon just missed Murphy's driven cross across the six-yard box before Humphrey blazed high and wide.
The action then became a succession of penalties, the first in the 64th minute. Griffiths raced on to Eoin Doyle's ball over the top and was forced out wide by Randolph.
The goalkeeper leaned into Griffiths as any defender would do before putting in a tackle and scooped the ball behind with his hand but was stunned to see O'Reilly deliver a yellow card.
Griffiths converted with a powerful strike into the corner just out of Randolph's reach.
Motherwell were handed a chance to pull one back in the 72nd minute when McPake climbed over Higdon to head away. But the home fans knew it was not their night when Higdon, the SPL's top scorer, blasted over the bar.
And O'Reilly confirmed their instincts two minutes later when he penalised Hammell for a challenge on Wotherspoon on the edge of the box with the Motherwell player insistent he got the ball as he went to ground.
Griffiths put his penalty in the exact same spot with Randolph again just out of reach. It proved O'Reilly's last major intervention. He appeared to be indulging in a long lecture of Motherwell manager Stuart McCall but it turned out he was finished for the night and was duly replaced by the fourth official.
Motherwell, with Omar Daley and Bob McHugh, were also done and the vast majority of home fans decided to get out of the freezing conditions long before Hibs substitute Handling slid home Wotherspoon's cutback six minutes into injury-time.