Team Sky's Thomas came home 21 seconds behind Spain's Bilbao (Astana), who staged a heroic solo effort 12 kilometres from the finish to triumph.
"Throughout the race I was never thinking about the end result, it was always about the next day or the next climb". "It's an unbelievable feeling to win and I think it will really start to sink in tonight".
"Ive been feeling good all year", the Irishman said after the race.
He follows fellow former British winners Brian Robinson, Robert Millar, Sir Bradley Wiggins and Chris Froome in to the history books.
It came on a 110 kilometres stage from Frontenex which is nearly a carbon copy of this year's Tour de France stage 11.
Yates said: "The Tour de France has been my main goal for the whole season".
He said it was learning from the previous days that helped him take victory on St Gervais Mont Blanc, delaying his attack to claim the stage win. We're getting closer and closer so I'm happy to get confidence from this race.
"Hopefully the authorities can just get their act together and have a decision, but I've got 100 per cent faith in him".
"My role in the team will be as one of the protected guys, Froome is going to be one of the leaders". France's Romain Bardet, of AG2R, jumped to third from seventh overnight and is at 2min 01sec.
England's Adam Yates, who's twin Simon wore the pink jersey at the Giro d'Italia for 13 stages in May, was third on the day at 15 seconds.
Navarro finished second, four seconds back, with Romain Bardet completing the podium, nine seconds off the pace.
Thomas is next due to race in the National Road Race championships in Northumberland where he is down to do the time trial (29 June) and the road race (1 July).