Germany's Laura Lindemann won a sprint finish in the final leg, narrowly edging out the United States in silver and Great Britain in bronze, who were separated in a photo finish.
Britain had initially been awarded the silver, but the decision was overturned minutes later.
The relay is a four-person sprint triathlon, with two men and two women completing a 300-metre swim, a seven-kilometre (4.3-mile) bike ride and a 1.8km run.
The Seine was used for the swim on Monday, as it was for the men's and women's individual triathlon last Wednesday.
But the river has been dogged by pollution problems despite a 1.4 billion euros (£1.9bn) upgrade to improve the Paris sewerage and water treatment system.
No athletes' training in the Seine has been possible since the start of the Games after the water repeatedly failed water tests, with bacteria levels above authorised limits.
On the eve of the mixed relay, the Belgian National Olympic Committee (COIB) revealed that Claire Michel had fallen sick after the women's triathlon last week.
"The COIB and Belgian Triathlon hope that the lessons will be learned for future triathlon competitions at the Olympics," the committee said in a statement.
The Belgian team withdrew from Monday's relay event as a result.
The Paris 2024 organising committee said in a statement that testing on the day of the individual triathlon last week had shown that the quality of the water was "very good" based on World Triathlon's criteria.
"The decision on whether to proceed with an event is taken by the international federation, World Triathlon, in coordination with Paris 2024, and based on the test results and a range of (notably health) criteria," it said.
"Paris 2024 wishes to remind everyone that the health and wellbeing of athletes is our top priority," it added.