The 25-year-old Chicago Red Stars forward scored her second goal in three games when she broke the deadlock in the 11th minute before netting again before the break and again to seal her hat-trick in the 69th minute.
Kerr added her fourth in the 83rd minute as Australia headed for the knockout stages as she moved level with United States' Alex Morgan as the top-scorer at this World Cup with five goals.
Australia skipper Kerr saw Jamaica goalkeeper Nicole McClure off her line and looped in a header after an inch-perfect cross from the left with 11 minutes on the clock.
Kerr kept up her prolific form when she nodded in the second after a simple ball was sent in from the right in the 41st minute.
Jamaica pulled one back - their first-ever goal at a Women's World Cup - when half-time substitute Havana Solaun coolly rounded the goalkeeper to roll the ball into the corner four minutes into the second half.
Khadija Shaw went close for the Reggae Girlz in the 54th minute but her strike flew over the crossbar. Shaw went close again 10 minutes later, evading two challenges before drilling a long-range strike which again rose over the bar.
However, it was Australia who found the net again and Kerr who claimed her hat-trick in the 69th minute.
Kerr had a penalty shout turned down by VAR as the match entered its last 10 minutes but added her fourth in the 83rd minute when McClure panicked and kicked the air instead of the ball when attempting a clearance.
Marta's late penalty handed Brazil a narrow 1-0 win over Italy to secure progress into the last 16 and earned her place as the record scorer at the finals.
The 33-year-old Orlando Pride forward, playing in her sixth World Cup, slotted in with 15 minutes left to settle the Group C clash in Valenciennes.
Marta's goal saw her past the mark of 16 set by Germany forward Miroslav Klose in the men's tournament.
A surprise 3-2 loss to Australia in their last match had left Brazil needing a positive result to make sure of progress to the knockout stage, while the Italians were aiming to record a third-straight win having defeated Jamaica 5-0 in Reims.
Italy had an early chance on the break, but Barbara Bonansea's shot from the edge of the box was saved behind by Brazil goalkeeper Barbara.
At the other end, Juventus stopper Laura Giuliani pushed a flick by Debinha from a corner over.
On the half-hour, Italy saw a goal from Juventus forward Cristiana Girelli ruled out for offside before Bonansea's close-range volley was blocked by quick reaction from the agile Brazil keeper.
Brazil almost broke the deadlock early in the second half when Andressinha's curling 20-yard free-kick clipped the top of the crossbar.
Bordeaux defender Kathellen headed wide from a free-kick before Brazil were awarded a penalty with 15 minutes left.
North Carolina Courage forward Debinha was adjudged to have been barged over by Atletico Madrid's Elena Linari as she broke into the left side of the box.
Marta made no mistake from the spot, sending the goalkeeper the wrong way as she slotted in a record 17th goal at the World Cup finals.
Milan midfielder Valentina Bergamaschi had a late chance for the Italians, but failed to make decent contact with the ball to test Barbara.
Australia's 4-1 win over Jamaica saw Brazil finish third in the table, as Italy - also with six points - topped the group on goal difference.
Brazil progress to the last 16 as one of the best third-placed sides, but will have to wait to find out who they face next - as will the Italians.
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