Kerr struck twice either side of the interval as Australia finished second in Group C. They pipped third-placed Brazil on goals scored to set up a meeting with Norway for a place in the quarter-finals.
Jamaica bagged their first goal of the tournament through Havana Solaun but finished bottom of the Group after three defeats.
Italy topped Group C on goal difference with six points despite a 1-0 defeat against Brazil.
Kerr scored her second goal of the tournament with a header after 11 minutes to put the Matildas in the driving seat on a stiflingly hot night at the Stade des Alves.
Kerr doubled the tally three minutes before the break with another header after being left unmarked in the area.
Halftime substitute Solaun reduced the arrears as she netted Jamaica’s first women’s World Cup goal after collecting a perfect through ball from Khadija Shaw in the 49th minute.
But Kerr became the first Australian to score a hat-trick in a senior World Cup with a clinical finish after a defensive blunder by the Jamaicans.
She added a fourth seven minutes from time and that final goal allowed them to leapfrog Brazil on goals scored in the standings.
“One to tell my kids about," said Kerr.
“Any time you break a record, especially for your country, it is an amazing feeling.”
(Writing by Julien Pretot, editing by Pritha Sarkar)
