Sjöström, timing 57.32sec, edged her way to victory ahead of British rival Francesca Halsall (57.40), with veteran compatriot Therese Alshammar taking bronze for Sweden.
"My whole season before the European Championships was really bad, and I'm very surprised I am about my results here in Budapest," admitted Sjöström.
Halsall had to be content with passing Alshammar on the second lap.
"Maybe I could have done better if I would have been more rested," she said. "I knew that Therese Alshammar would go out very fast, and my strength is the second lap.
"I'm happy that I managed to catch her on the very last metres of the race."
Russia's Anastasia Chaun took gold in the women's 200m breaststroke in 2min 23.50sec ahead of Norwegian Sara Nordenstam with Rikke Moeller Pedersen of Denmark taking bronze.
"I had never reckoned with a medal before the European Championships," said Chaun.
"I certainly benefited from the absence of my team-mate Yulia Efimova in this event. She was ruled out of the 200 metres because of a shoulder injury."