The 34-year-old Cristiane, replacing injured six-time FIFA World Player of the Year Marta, netted in the 15th, 50th and 64th minute in front of a 17,000 crowd at the Stade des Alpes in Grenoble.
Cristiane completed her triple with a fine free kick in the 64th minute as Brazil ended a poor recent run of nine straight defeats.
The match was also notable for the appearance of midfielder Formiga for Brazil, becoming the first player to appear at seven Women’s World Cups and at 41 years and 98 days the oldest to appear in the tournament.
“Our attack was a huge point of satisfaction,” Brazil coach Vadao said after the convincing victory.
“Especially Cristiane, who the coaching staff has always believed in despite her injuries.”
Vadao was also hopeful Marta would be available for Thursday’s game against Australia in Montpellier, which takes on added importance after the opening loss for the Matildas.
Italy end 20-year wait with shock win
It sparked scenes of wild celebration as the Italy bench emptied and Bonansea was hoisted high into the air by her jubilant teammates.
Ranked sixth in the world and with one of the world’s best players in the team in captain Sam Kerr, Australia had gone into the match at the Stade du Hainaut full of confidence and it did not take long for Kerr to make an impression.
She won a penalty after being pulled down by Italian counterpart Sara Gama and although her initial weak effort was saved by Laura Guiliana, Kerr scored on the rebound.
She celebrated in the style of former Australian international Tim Cahill, punching the corner flag, much to his appreciation, which he shared on social media.
Bonansea, who had an earlier effort ruled out for marginal offside by VAR, leveled for Italy, who are nine places below Australia in the world rankings, on 56 minutes after a defensive howler by Clare Polkinghorne, who was caught napping in possession.
Italy had a second effort ruled out for offside with nine minutes remaining after Daniela Sabatino finished neatly, but Bonansea connected with a free kick to beat Lydia Williams in the Australian goal for the winner.
Italy boss Milena Bertolini told reporters: “When it comes to teamwork, they are truly the strongest team at this tournament and that’s what will make the difference — team spirit. It made the difference. We suffered a lot, but the Italian team spirit came through.”
England edge old rivals Scotland
The latest edition of the oldest rivalry in world football looked set to be a one-sided affair as a penalty from Nikita Parris and a curled effort from Ellen White put England 2-0 ahead at halftime, but after the break the Scots rallied to pull a goal back from Claire Emslie with 11 minutes remaining.
“We set standards and the players have to keep meeting them,” he told BBC Sport.
“We cannot drop below those standards and if we do we get performances like that second half. We have to be relentless.”
England took the lead courtesy of a VAR decision to award a penalty after a cross from Fran Kirby hit the outstretched arm of Nicole Docherty.
The lively Parris converted past Lee Alexander, who had little chance when White scored the second on 40 minutes.
Alexander kept Scotland in the game with some fine saves, while England also had two efforts chalked off for offside.
But Scotland, making a first appearance in the finals, showed great spirit and gave its fans in the Allianz Arena late hope as Emslie reacted smartly to a Lisa Evans pass to cut the deficit.
“We can take a lot of positives,” said Scotland coach Shelley Kerr, with her team next facing Japan in Rennes while England is taking on Argentina in Le Havre.