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A former ski jumper, Roglic had consolidated his grip on the overall leader's yellow jersey when finishing second in Saturday's penultimate stage.
And he did enough on Sunday to head the closing general classification by eight seconds from Colombian Egan Bernal of Team Sky with Australian Richie Porte, last year's Romandie winner, 35sec back in third.
The 28-year-old Roglic, successful already this season of the Tour of the Basque Country, won a stage on the Tour de France in 2017 and a stage on the Giro in 2016.
In his previous career, Roglic won a junior world ski jump title in 2007.