Team Garmin's Millar finished 26 seconds behind Team Radioshack's Jan Brajkovic, who completed the journey in 1hr 1min 51sec, and it is the Slovenian who is wearing the yellow jersey after three stages.
Millar, who is targeting overall victory here, lies second overall, 36 seconds adrift of Brajkovic, and 14 ahead of the promising 21-year-old American Tejay van Garderen.
Welshman Geraint Thomas completed his third successive top-ten finish to close in seventh, enough to place him fifth overall. Two-time Tour de France winner Alberto Contador slipped from first to fourth.
Millar, a time trial specialist, is looking forward to the mountain stages on the Criterium du Dauphine, as a warm-up race for the Tour de France next month.
"I feel much better in the mountains than last year. That is why I am looking forward to this week's mountain stages," said Millar. "I will see if I can keep up with the climbers. Here, with the exception of Contador, the level is quite homogenous. I can take my chance. I need a result, I need a win."