The Dutch champion, who rides for the Rabobank team, was second in the stage, just losing the final sprint to the Colombian Santiago Botero, but that was good enough to give him the leader's jersey.
Boogerd, fifth in last year's Tour de France, and Botero broke away on a climb some 15km (9 miles) from the finish of the 187.9-km stage from Cusset to Firminy.
Botero, of the Spanish Kelme team, and Boogerd finished almost half a minute ahead of the next group of riders, which included the Dutchman's Rabobank team-mates Marc Wauters of Belgium and his compatriot Maarten den Bakker.
O'Grady lost ground in the last few kilometres and finished several minutes behind the leaders, dropping out of the top 10 overall. The Australian said the course had been tiring and he could not keep up. "I was dead," he said.
Boogerd is 16 seconds ahead of the Belgian veteran Andrei Tchmil, the leader after the first stage and second since then. Wauters is third, a further eight seconds behind.
"The team decided to go for the lead today rather than wait until Saturday at Valberg. When Botero broke away I felt it was a good escape. I know him and he's anything but a lazy guy. Now we have the best chances of winning," Boogerd said.
Massimo Strazzer, of Italy, beat the pack in a sprint finish yesterday to win the second stage of the Tirreno-Adriatico race, a prelude to the Milan to San Remo classic on 20 March that opens the World Cup circuit.
The Latvian rider Romans Vainsteins, a second-year professional, was third and held on to his overall lead. The top-ranked Michele Bartoli was 14th and the Italian remained second to Vainsteins, five seconds behind.
Strazzer completed the mostly flat 178km stage that ran north from Sorrento, near Naples, to Santa Maria Capua Vetere in 4hr 43min 15sec. However, he did not do enough work to make up for his poor showing in the opening leg and stands 77th overall, trailing the leader by eight minutes.
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