Movistar rider Valverde, back this season after a two-year ban for his implication in the Operation Puerto blood-doping scandal, surged ahead in the final stretch after a short climb and held off second-placed Simon Gerrans of Australia.
Belgium's Gianni Meersman took third place while Briton Bradley Wiggins retained the overall leader's yellow jersey.
"It was really hard today, everybody was knackered," said Team Sky rider Wiggins, who leads Americans Levi Leipheimer and Tejay van Garderen by six and 11 seconds respectively.
Valverde is sixth, 20 seconds off the pace after his win gave him a 10-second time bonus.
Luxembourg's Andy Schleck, who will be awarded the 2010 Tour de France title after Alberto Contador was stripped of his victory following a failed dope test, pulled out of the race before the start, citing gastroenteritis.
His Radioshack Nissan sports director Alain Gallopin told reporters on Tuesday that Schleck would probably take part in the Tour of Catalunya from March 19-25 to make up for lost time on the bike.
Schleck, however, was already well out of contention after another mediocre time-trial display in the opening stage and finishing some 11 minutes off the pace in the second stage on Monday.
On a cold, dark day in central France, a three-man breakaway built up a five-minute gap but Team Sky worked at the front of the peloton to chase them down and Frenchman Jimmy Engoulvent was caught six kilometres from the line.
Uzbekistan's Sergey Lagutin pulled away in the final section, a 5.2-km climb at an average gradient of 3.9 percent , but he failed to sustain the pace.
Valverde, who had looked forward to the final climb, surged ahead and beat Gerrans to add to his Tour of Andalusia and Tour Down Under victories.