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.
"I knew I had about one minute 20 seconds to lose on Yatesy so at 200 (metres) to go, when they started sprinting for the win, I was relieved", Thomas was quoted as saying by the BBC.
"I think these four days are the hardest four days I've raced in a one-week stage race", said Thomas. It's a massive race and it's an incredible feeling. I had to chase back on.
He follows fellow former British winners Brian Robinson, Robert Millar, Sir Bradley Wiggins and Chris Froome in to the history books. Bilbao made his move late on during the gruelling stage that is nearly the same as stage 11 in the Tour de France next month, with four major climbs and a summit finish at la Rosiere.
Yates said: "The Tour de France has been my main goal for the whole season".
"It's not a great situation for him, the team or just cycling in general", Thomas said. I just made that final move towards the end.
It gave them a 19 second lead over Team Sunweb and a 27 second advantage over Quick-Step Floors. "I managed to get a few more bonus seconds which is good".
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