Wolves had opened their League One campaign with a draw at Preston and then suffered Capital One Cup embarrassment against Morecambe in midweek.
But Kenny Jackett's men put Gillingham to the sword with Griffths, Lee Evans and Bakary Sako putting them 3-0 up at half-time, when they left to standing ovation.
The newly-relegated Wolves played in front of a supporters banner which read "this is our love, and it knows no division" - and Griffiths sent the loyal fans home happy by wrapping up the win with a second-half penalty.
Free-scoring Leyton Orient are top of the embryonic league table after 3-0 victory over Shrewsbury, with two goals David Mooney and a third from Moses Odubajo securing the three points.
Second-placed Peterborough have also opened their league campaign with back-to-back wins after coming from a goal down to beat Notts County 4-2 at Meadow Lane.
After Dean Leacock had put the hosts ahead, Tommy Rowe, Tyrone Barnett, Grant McCann and Britt Assombolonga sealed Peterborough's win before a late consolation penalty from Yoann Arquin.
Walsall and Colchester have both started their season with back-to-back league wins.
James Baxendale's goal was enough for Walsall to beat Oldham and Gavin Massey's strike earned Colchester the win against Port Vale.
Bradford won 4-0 to inflict another league drubbing on Carlisle suffered a second drubbing, following their 5-1 home defeat to Leyton Orient on the opening weekend.
Carlisle did beat Blackburn in the League Cup in midweek but they were 3-0 down inside nine minuteson Saturday with Mark Yeates, Nahki Wells and James Hanson putting Bradford in control before Gary Jones added a fourth.
Brentford followed up their opening-day draw with a 3-1 win against Sheffield United.
Summer signing Will Grigg scored twice after Adam Forshaw's opener had been cancelled out by Neill Collins' header.
Tranmere snatched a point in a dramatic 3-3 draw with Crawley thanks to Ryan Lowe's injury-time equaliser.
Joe Thompson's double gave Rovers a half-time lead but Billy Clarke and a second from Joe Walsh turned the tide in Crawley's favour before Lowe's equaliser.
Patrick Bamford's goal was enough for MK Dons to beat Crewe, Swindon beat Stevenage with a strike from Massimo Luongo while Rotherham and Preston played out a goalless draw.