Victory meant the World Cup finalists had won both their opening Group B games following a convincing 4-0 defeat of the Netherlands on Friday.
France goalkeeper Mike Maignan, however, had to make two fine saves late on, including a superb stop from Nathan Collins' header, to deny Ireland a draw in the hosts' opening qualifier.
Bayern Munich defender Pavard, making his first appearance for France since their opening group game of the World Cup in Qatar, struck five minutes into the second half after seizing on a loose pass across the face of his own goal by Ireland's Josh Cullen.
But third-ranked France were pushed hard by an Ireland side 45 places below them in the FIFA standings.
"It's never easy against a team like that who keep the pressure on," said France coach Didier Deschamps.
"Six points, well, the results are great. Congratulations to the group (France squad), but the road is still long."
Deschamps, turning to Pavard, added: "He's on the way back up and it's him who won the game for us.
"Anyone can struggle for form and now he's coming back to his best."
Ireland winger Chiedozie Ogbene hailed his side's performance by saying: "We should be very proud, we matched one of the best teams in the world and the future is bright."
Seamus Coleman overcame a thigh injury to captain Ireland in one of six changes to the side that beat Latvia 3-2 in a friendly last Wednesday.
France dominated the first half but created few clear chances, with Collins preventing Giroud from capitalising on Randal Kolo Muani's clever back-heeled pass.
Yet for all their superiority, France were indebted to an Ireland error when going ahead in the 50th minute.
Cullen's over-ambitious pass was pounced on by Pavard, whose powerful shot past goalkeeper Gavin Bazunu went in off the underside of the crossbar.
But with Coleman leading a fine defensive effort that kept superstar France striker Kylian Mbappe quiet, the game remained in the balance.
Ireland almost equalised wen substitute Kounde headed the ball towards his own net, only for Maignan to make a fine stop.
Moments later, Maignan made a truly world-class save from a Collins header before France survived three minutes of added-on time.
"Mike is Mike," said Deschamps. "It's not easy taking over (from Hugo Lloris) but ever since he has been with us he's been great."