The masterstroke from coach Didier Deschamps at the break unshackled France's attackers, who had struggled to get a hold on the game early on after a Robbie Brady penalty in the second minute, the fastest goal so far at this year's tournament.
Griezmann struck either side of the hour mark to the relief of the nervous home fans before Ireland had defender Shane Duffy sent off after 66 minutes for bringing down the flying forward.
France, who have scored 11 of their 12 goals at European Championship finals after halftime, will next play England or Iceland, who meet on Monday, at the Stade de France next Sunday.
"We have difficulties getting into games, we saw that again today, and that's something we have to work on," said Griezmann.
"Finding ourselves trailing made it difficult but we showed we've got heart. Things were said in the dressing room at halftime and in the second half it was a different France team."
BAD START
It was the worst possible start for France when serial offender Paul Pogba, responsible for conceding two of his country's last four penalties, clumsily barged over Shane Long in the area and allowed Brady to put Ireland into an early lead.
Finding themselves behind for the first time at the tournament, the hosts seemed to lack the urgency to gain control in a stop-start first half.
Their best chance fell to Griezmann who headed over the bar from close range, while a late strike by Dimitri Payet whacked into the Irish defenders who bravely guarded their goal.
With the home side's spirit sapping, Ireland sensed an upset and retribution for the last time the sides met in 2009, a World Cup qualifier which France won controversially after a handball from striker Thierry Henry helped set up the decisive goal.
But for all their hard work in defence, the Irish did not really look like consolidating their lead.
On one rare foray, France keeper Hugo Lloris -- captaining his country for a record 55th time -- was called into action to push a bouncing shot from striker Daryl Murphy wide.
Deschamps changed things after the break, pushing Griezmann into a more central role behind strike partner Olivier Giroud and replacing holding midfielder N'Golo Kante with pacey winger Kingsley Coman, which allowed playmaker Pogba to take the reins in the middle of the pitch.
The strategy paid dividends immediately as France stretched a tiring Ireland. Griezmann equalised in the 58th minute from a Bacary Sagna cross and fired his team in front three minutes later when Giroud nodded the ball down into his path.
NOT EASY
"With Griezmann closer to Giroud up front and Kingsley (Coman)'s presence, we made them suffer," said Deschamps.
"It's not easy for any team here and it was not easy for us. We did not have the right not to qualify and that made it complicated for us but we're through."
Another surging run from Griezmann saw him chopped down on the edge of the area by Duffy, earning the defender a red card as the game started to look beyond the Irish.
The packed home support -- who booed their team as they trudged off at halftime -- broke into a deafening 'Marseillaise' and cheered France all the way to their first knockout stage win at a Euro finals since winning the trophy in 2000.
On a sour note, though, Kante and defender Adil Rami picked up yellow cards and will be suspended for the quarter-final.
"We really have to start our next match better. We must not underestimate anybody," said defender Patrice Evra.
"We'll be without Adil and N'Golo Kante but we're a group of 23, we'll be all right."
(Editing by Julien Pretot and Ken Ferris)
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