Goals from Carli Lloyd and Alex Morgan saw the United States beat New Zealand, while Germany were far too strong for Zimbabwe.
Defending champions the United States kicked-off their Olympic women's football tournament with a win over New Zealand, while Germany put six goals past a hapless Zimbabwe.
USA, winner of gold in London in 2012, started things brightly against New Zealand on Wednesday with a goal inside nine minutes through captain Carli Lloyd.
It took USA just seconds to double their lead in the second half, with Alex Morgan finding the net to wrap up a 2-0 win in Belo Horizonte.
Germany meanwhile scored four second-half goals to seal a 6-1 victory over Zimbabwe, with Melanie Behringer netting a brace for the 2015 Women's World Cup semi-finalists.
Canada got off to a perfect start with a 2-0 win over Australia despite having just 10 players for the majority of the game, Janine Beckie and Christine Sinclair scoring in each half.
Hosts Brazil secured a 3-0 win over China PR, Sweden edged South Africa 1-0 courtesy of Nilla Fischer's 75th minute goal, and France made easy work of Colombia, winning 4-0.
Australia, ranked fifth in the world, were favourites going into their Group F opener with Canada, but Beckie was on hand to tap home just 20 seconds into the first half for the North Americans following a defensive error, which was the fastest goal in Olympic women's football history.
PLAYER OF THE DAY
BRAZIL OPEN WITH A WIN
Monica scored Brazil's opener to help the host team defeat China, even if it was not the prettiest of finishes.
"I am very happy because of the work we are doing. There is nothing better than to begin with triumph. My sensation when I scored the first goal was complete happiness," she said.
"It was a close game and it doesn't matter if the goal was not so beautiful, it is a goal."
Matchday two takes place on Saturday with the pick of the games seeing USA come up against France in Group G, while Australia tackle Germany in Group F.