Pogba came on at halftime and immediately injected new life into a French midfield that had struggled to create chances against the sort of well-organised, compact team which has been typical of the so-called minnows at Euro 2016.
Griezmann, brought on midway through the second half, went one better when he ended 90 minutes of stubborn Albanian resistance by heading the first French goal.
If France coach Didier Deschamps wanted to see how his team would cope without the pair, who both disappointed in their opening 2-1 win over Romania, then he did not have to wait long for the answer.
France barely created a clearcut chance in a poor first-half and were jeered off at the break.
Pogba has struggled to recreate the impact he has with Juventus when he plays for the national team while Griezmann may be suffering the after effects of a long, exhausting season at Atletico Madrid under the demanding leadership of Diego Simeone.
Nobody, however, had expected either player to be left out altogether and there were more than a few raised eyebrows when both were missing from the starting lineup.
Had Deschamps simply decided that he could afford to rest them against the Euro 2016 debutants?
Or was he about to join the long list of national team coaches who, for whatever reason, have felt they can dispense with some of their country's top players?
Whatever the motive, it did not pay off.
Deschamps himself agreed that the two had made the difference.
"We didn't do enough in the first half but the second half was a lot better. The players who came on made a difference," he said.
Griezmann said: "The coach told me before the match that I would not start and I was determined to help the team the best I could when I came on.
"That goal will help me a lot. What I have to do is concentrate on working close to the box because that's where I'm the most dangerous."
For Euro debutants Albania, the match was the second harsh lesson in the realities of major tournaments and left them without a point or a goal scored.
Against Switzerland on Saturday, a goalkeeping error, a first-half sending-off and two bad misses cost them at least a point as they lost 1-0.
They seemed to have weathered the French storm on Wednesday until a momentary loss of concentration cost them again.
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