Back in the tournament after a 20-year absence, the Azzurre top Group C with six points ahead of Brazil and Australia who have three. Jamaica have yet to earn a point.
Girelli opened the scoring with a retaken, VAR-awarded penalty before netting again either side of the interval.
Galli rounded off the victory with two goals after coming on midway through the second half, capping a second win after Italy defeated Australia 2-1 in the opening game.
"We wanted to move on in the group phase and to do this after two matches is a great satisfaction for us," said Italy coach Milena Bertolini after her players achieved what the Azzurri failed to do in the last three men's World Cups when they went out in the group phase in 2010 and 2014 and failed to qualify for the 2018 finals.
"The girls were awesome, to stay with their feet well planted on the ground, considering all of the attention and coverage we’re getting back home.
"These women are a very close-knit group and have reached a high level of maturity."
Her Jamaica counterpart drew positives from the experience after the result followed a 3-0 defeat to Brazil.
"This is bigger than the World Cup; this is just part of the journey; this is a learning experience," Hue Menzies said.
"I’m telling you, if we keep these players together, it will be different. When you come here, you see excellence, and that’s what we have to be."
Schools from around Reims brought their students to the game, giving the atmosphere an upbeat feel.
Three days after the United States thrashed Thailand 13-0, the Stade Auguste Delaune crowd were treated to more champagne football.
Italy went ahead after 12 minutes when Girelli converted a penalty on her second attempt, having had to retake it after keeper Sydney Schneider had stepped off her line.
The penalty was awarded following a VAR review after Allyson Swaby brought down Barbara Bonansea.
Girelli doubled the tally in the 25th by latching on to a corner before securing her hat-trick shortly after the restart, jumping higher than Schneider to head home.
Galli added the fourth shortly after coming on for Valentina Bergamaschi with a thunderous 25-metre strike in the 71st.
Ten minutes later, she rounded Schneider before tapping the ball into the net to wrap up an impressive win.
Italy next play Brazil, with Jamaica facing Australia.
(Writing by Julien Pretot; Editing by Ken Ferris and Clare Fallon)
