Having cruised through their 2018 FIFA World Cup qualification campaign, the hosts were in fine form at Stade de France, with Griezmann at the heart of a vibrant first-half performance in France's first meeting with Wales since 1982.
After a lively opening, in which Kylian Mbappe struck the woodwork, Griezmann took matters into his own hands 18 minutes in - volleying home from Corentin Tolisso's pinpoint pass - though Wales goalkeeper Wayne Hennessey should have done better.
Shorn of the injured Gareth Bale, Wales - in their first match since missing out on a place in the FIFA World Cup qualification play-offs - improved after the interval, with Steve Mandanda at his best to deny Aaron Ramsey from point-blank range.
Any hopes of a comeback for Chris Coleman's side were ended with 19 minutes remaining, however, as Giroud tucked home in typically composed fashion.
Samuel Umtiti and Benjamin Pavard almost added gloss to the triumph late on, but their misses mattered little, as Wales's five-match unbeaten run on the road was brought to a halt.
France should have been ahead inside eight minutes - Blaise Matuidi and midfield partner Tolisso both wasteful from the edge of Wales's area.
Wales had Hennessey to thank moments later as he somehow turned Mbappe's strike onto the crossbar, though he was then beaten far too easily for France's opener.
Griezmann did well to connect with Tolisso's delicately-weighted throughball, the Atletico Madrid man executing an acrobatic over-the-shoulder volley which, despite lacking any real power, slipped through Hennessey's grasp.
France continued to cause havoc - Ashley Williams ensuring Ben Davies's error did not prove costly when Kinglsey Coman easily shrugged off the Tottenham Hotspur defender.
For all France's domination, though, Wales could have been level on 36 minutes had Chris Gunter made a better connection with Neil Taylor's cross.
Hennessey atoned for his earlier error with a superb stop minutes after the restart, lunging to his left to keep out Giroud's venomous shot.
Griezmann's game came to an end just after the hour, France's goalscorer receiving a standing ovation as he made way for the in-form Nabil Fekir.
Fekir's impact was instantaneous when his brilliant corner found fellow substitute Steven N'Zonzi, who failed to direct his header on target.
N'Zonzi's miss almost proved costly, Mandanda pulling off an instinctive save to prevent Ramsey restoring parity after fine play from Wales debutant David Brooks.
Wales's resurgence was short-lived though - Giroud on hand to squeeze in a cute finish after great work from Mbappe.
France could have made it three in the closing stages, with both Umtiti and Pavard both striking the upright as Les Bleus eased to a comfortable win.