Cristiane started in place of Marta, who has not recovered from a thigh injury.
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.
Reggae Girlz goalkeeper Sydney Schneider made a string of good saves including a dive to gather Andressa's weak 38th-minute penalty.
Formiga, appearing in a record seventh World Cup and, at 41 years and 98 days the oldest woman to play in the competition, controlled midfield.
Paris Saint-Germain defender Daiane, who had flown in from Brazil on Friday to replace injured Erika, came on in the 76th minute.