Björn Seelinger broke a personal record on his leg in the semi-final when Sweden reached the final with a time of 48.07.
Once there, he was the first in the water when Sweden finished third.
Seelinger replaced Robin Hanson as second in a time of 48.09.
The 21-year-old then dropped a few places, although Hanson put in a good effort.
Then superstar Sarah Sjöström took over and swam Sweden up to medal position from first place.
There, the newly minted gold medalist from the 100-meter butterfly took over and secured her and Sweden's second medal of the evening.
She finished third, behind victorious France and Great Britain after a magnificent finish.
The bronze is Sweden's second team medal in Rome during the European Championships, after the women's silver in the team medal.