The Besiktas striker hit the target with a left-foot strike after 32 minutes when midfielder Ozan Tufan put him through with a headed assist.
Sweden then took control in the second half to earn a deserved 74th minute equaliser from Andreas Granqvist, who scored from close range.
Both sides had their chances to earn a winner but it was Tosun who proved the decisive figure nine minutes from time, heading home Selcuk Inan's cross to leave the visiting goalkeeper Robin Olsen helpless.
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(Reporting by Ece Toksabay, editing by Ian Chadband)
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