Lindsey Horan netted the tournament's fastest goal after three minutes and Jonna Andersson scored an own goal as the US beat the record for most goals (18) in the women's World Cup group stage.
Sweden, who were also qualified before kickoff, finished second in the group with six points and will face Canada for a place in the quarter-finals.
The US did not concede a goal in the group phase.
The US made a fast start when Horan tapped in the opening goal from close range from Megan Rapinoe's corner.
That equalled Norway's record group-stage tally of 17 set in 1995 but despite Sweden's determined resistance, the mark seemed destined to be beaten at the Stade Oceane.
Five minutes into the second half, Heath's header took a deflection off Andersson as the U.S. doubled their lead.
The goal was confirmed after a VAR review which ruled that Heath was not offside.
Chile beat Thailand 2-0 to finish third in the group but were eliminated from the tournament. Thailand ended without a point.
Cameroon qualified for the women's World Cup last 16 when Ajara Nchout earned them a 2-1 win over New Zealand with the last kick of their Group E match on Thursday. Meanwhile, the Netherlands' Anouk Dekker and Lineth Beerensteyn breached Canada's normally rock-solid defence with second-half goals to secure a 2-1 win that earned them top spot in Group E.
