Cristiane started in place of Marta, who has not recovered from a thigh injury.
Teammate Formiga became the oldest player to appear in the women's finals, at the age of 41 years and 98 days, and also the first to appear in seven editions of the tournament. The 34-year-old, collecting her 139th cap, headed in the opener after 15 minutes, scooped a rebound over the line after 54 minutes and curled a free-kick in off the underside of the bar after 64 minutes.
While Jamaica's pace sometimes troubled the Brazilian defence, Brazil could have won by more.
Bonansea scored the equalizer for the 15th-ranked Italians in the 56th minute and headed home the victor past goalkeeper Lydia Williams in the fifth minute of stoppage time.
The sixth-ranked Matildas struck first on Sam Kerr's 22nd-minute goal. "But it only holds real value if we get out of the group, so let's wait and see how great it is", Italy coach Milena Bertolini said.
Jamaica have a star in the making in the form of 22-year-old Khadija Shaw who has scored 26 goals in only 30 appearances for her nation and is as of now the most astounding scoring player to ever show up for Jamaica.
"It's so wonderful. I hope we can qualify for the knockout stage because these two goals are meant to help us do just that".
Portugal's Cristiano Ronaldo holds the men's record, having scored three goals in a 3-3 draw with Spain in the 2018 World Cup in Russian Federation at 33 years and 130 days.
Daniela Sabatino had a goal ruled out for offside, but Italy were not to be denied a second, with Bonansea their hero in the dying embers with a fantastic header to clinch the points.