Griffiths was a constant menace and finished off a slick move 30 seconds before half-time to allow Hibs fans some respite from the taunting of the visitors to Easter Road.
Alan Maybury had earlier gifted his former club the opener on his Hibernian debut when Andrew Driver pounced on his short header back to goalkeeper Ben Williams, and Hearts stretched their unbeaten derby run to 12 games.
But Hibs showed the character lacking in their 5-1 Hampden defeat as they matched Hearts in a bad-tempered contest that produced six yellow cards and could have seen more.
Maybury and former Coventry midfielder Gary Deegan made their debuts to make it five summer signings in the starting line-up for Hibs.
But there were plenty of reminders of the cup final for the green half of the city with Hearts fans arriving in party mood with beach balls and balloons, some of them shaped in the figure five.
Manager Pat Fenlon continued to suffer from May as he completed a touchline ban served for making a gesture as Hearts fans taunted him at Hampden. Hearts have also undergone change with John McGlynn returning to the club as manager and the likes of Rudi Skacel and Ian Black departed amid cutbacks.
Griffiths got Hibs off to a lively start and he created the first opportunity with an inswinging free-kick that David Wotherspoon headed towards the far corner but Jamie MacDonald got down well to hold.
Williams pushed Darren Barr's 25-yard strike wide before Deegan was booked for a poor challenge on David Templeton.
Templeton showed his frustration moments later when he lashed out at James McPake after a foul and appeared to catch the Hibs captain in the chest but Willie Collum gave a free-kick and took no further action.
Templeton almost scored with the 30-yard effort but Williams did well to hold his powerful strike at full stretch.
The scrappy play was encapsulated in the 29th-minute opener. John Sutton and Ryan McGowan won headers deep inside Hibernian's half after MacDonald's kick-out but Maybury had time and space to head back to Williams. However, the Irishman was badly short and the alert Driver nipped in to steer it home.
Barr was booked for sliding in on Maybury and Deegan took a chance with another foul on Templeton.
Griffiths lifted Hibs when hit the outside of the post from a tight angle after running at Hearts down the left. And he netted Hibs' first of the season after Lewis Stevenson opened play up with a brilliant crossfield pass to Wotherspoon.
The midfielder cut inside and played the ball into Griffiths in space inside the penalty box and the on-loan Wolves striker poked the ball through MacDonald's legs before celebrating in front of the Hearts fans.
The second half started in similar fashion with Hearts defender Andy Webster booked when he kicked Eoin Doyle from behind before an injured-looking Stevenson was replaced by Jorge Claros.
Williams had a let-off when he missed Templeton's inswinging corner and Ryan McGowan flashed a header wide.
The home side were mostly on the front foot in the early stages of the half though.
McPake came close with two headers and Doyle dragged a shot wide after turning Webster.
Hearts brought on Mehdi Taouil and Arvydas Novikovas in a bid to find some creativity and they had a better spell although Hibs repelled their pressure, mainly from corners.
Hearts skipper Marius Zaliukas was booked for exchanging gestures with the home support and Maybury followed him for a challenge on Novikovas.
Hibs lost Griffiths to a knock and ended the game with a young strikeforce of Ross Caldwell and Danny Handling. The former soon had a header parried by MacDonald after a deep corner.
Paul Hanlon was the next man booked for a late challenge on McGowan and Deegan again avoided a second booking for pulling back Callum Paterson.
Both sides pushed for a winner in the final 10 minutes without creating chances.