Dutchman Slagter, of Team Blanco, made a late attack on the 139km route from Unley to Stirling to claim victory and reinforce his lead in the young rider classification.
Australian Matt Goss crossed the line at the uphill finish in second with world champion Phillipe Gilbert third.
“It’s incredible, I can’t believe it,” Slagter said.
“I saw on the screen that I was the first one. I thought they were coming… but I was the strongest, it’s incredible."
The victory was Team Blanco's first since the renaming of the team formerly known as Rabobank and with a time bonus secured by Slagter, he moved to within 14 seconds of Thomas, who finished fourth of the day.
Team Sky’s two-times Olympic track gold medallist was able to rely on the help of his team-mates, who repeatedly reeled in breakaways over the course of the stage.
“The boys had to ride really hard, they did an incredible job today,” Thomas said.
“It was a tough day so that’s mission accomplished I guess.”
Spanish rider Javier Moreno of Movistar lies in third on the general classification ahead of stage four of six on Friday, a route from Modbury to Tanunda.