BRASILIA - With 28 minutes remaining in Monday's game in Brasilia and the match goalless, Deschamps elected to send on Griezmann in place of Arsenal striker Olivier Giroud, and his impact was immediate.
The 23-year-old's entrance allowed Karim Benzema to move into his preferred central role from the left and within minutes he had teed up the Real Madrid striker for a shot that Victor Moses had to hack off the line.
Benzema's repositioning helped France gain a foothold in the final third and after weathering initial pressure, Nigeria finally cracked in the 79th minute when Paul Pogba headed in at a corner.
Griezmann then forced Nigeria captain Joseph Yobo to divert a Mathieu Valbuena cross into his own net in injury time, and Benzema was quick to express his gratitude for the Real Sociedad forward's contribution.
"Griezmann added something when he came on," said the France number 10 after his side's 2-0 win at the Mane Garrincha National Stadium.
"We found more space behind their defence, whereas in the first half, we weren't able to." Giroud had largely toiled in attack, despite several accomplished lay-offs, but his display was applauded both by Deschamps and goalkeeper Hugo Lloris.
"Olivier tapped, tapped, tapped against the defenders, and then the players who came on did the rest," said the France captain.
Giroud, meanwhile, sought to assert that Griezmann's entrance had not been the sole factor in swinging the match France's way.
"The substitutes coming on was beneficial," he said, using the plural - like Lloris - even though Moussa Sissoko did not replace Valbuena until the fourth minute of stoppage time.
"They capitalised on the work that had been done for an hour, an hour and a quarter."
While Benzema and Valbuena are effectively guaranteed starting berths in the French attack, Deschamps's experiments with Griezmann and Giroud in the remaining role have so far yielded mixed results.
With Griezmann alongside him on the left flank in France's opening game against Honduras, Benzema excelled, scoring twice and forcing an own goal from goalkeeper Noel Valladares in a 3-0 win.
When Giroud replaced Griezmann against Switzerland, France were even better, counter-attacking at pace to record a 5-2 win in which five different players - including all three forwards - scored.
Back in the team for the 0-0 draw against Ecuador, Griezmann shone in fits and starts, and it was not until Giroud came on in the second half that France threatened to unsettle their opponents' rugged defence.
But against Nigeria - another physically obdurate side - it was a different story, with Benzema looking disinterested on the left wing until Giroud's exit and Griezmann's arrival changed the game.
Deschamps echoed his players' thoughts when asked if he regretted not starting Griezmann over Giroud.
"They have different profiles," he said.
"You don't know and I don't know if it would have worked if Griezmann had started the match. The match lasts 90 minutes.
"Olivier acted as a focal point, produced some useful lay-offs, and brought his strength in the air, both offensively and defensively.
"There were two options. I could have started as we finished, but the important thing is that it goes well at the end and it finishes well for us." In the neat, incisive Griezmann and the tall, physically imposing Giroud, Deschamps has a two very different forwards at his disposal, but with Friday's quarter-final against Germany now looming into view, the composition of his attack remains a conundrum.