If the results hold up in another recount, which could last past Christmas, Rossi will have beaten Attorney General Gregoire in the closest gubernatorial election in Washington history.
The contest was the nation's last undecided race for governor.
Rossi had also won the regular count, but his 261-vote margin was so tiny that it triggered the automatic recount.
The Republicans called on Gregoire to concede and not drag the state through a third count that could take a month or more.
"As far as we're concerned, Dino has won. Dino has won twice," said a jubilant Rossi spokeswoman Mary Lane. "It remains to be seen what Christine Gregoire will do after losing two counts."
But even before the last big surge of ballots was tallied, the Democrats had signaled they would seek a hand recount in at least part of the state if Gregoire ended up on the short end. Democrats said afterward that they were still weighing their options.
"We haven't made a decision yet," Gregoire spokesman Chuck Hunter said. "We're stunned that it's a dead heat, going down to the wire."
Rossi, 45, a real estate millionaire and former state Senate budget chairman from the Seattle suburb of Sammamish, was hoping to become the first Republican since 1980 to get elected governor. He ran on a platform of change and job-creation.
Gregoire, 57, was hoping to become the state's second woman governor. She carried eight of the 39 counties, most notably the largest, King, which includes heavily Democratic Seattle. Gregoire was strongly backed by the women's movement and was best known for battling America's tobacco industry.
The winner succeeds retiring two-term Gov. Gary Locke on Jan. 12. Locke is the country's first Chinese-American governor.
During the two weeks since Election Day, the Bush White House dispatched its election experts to Washington, and the Democratic Governors Association offered to help finance a new hand recount of at least part of the state.
Secretary of State Sam Reed, the state's chief elections officer, said he plans to certify the machine recount on Tuesday. The campaigns or their parties have three business days to request a full or partial manual recount at their own expense.
Reed said he would probably direct that such a recount begin Dec. 6, and that the job could take as long as two weeks. If a partial recount changes the outcome, state law requires a manual recount in the rest of the state. That would extend the uncertainty past Christmas.
The Seattle area's heavily Democratic King County gave Gregoire a last-minute lift, but not enough to put her over the top.
More than 700 previously uncounted ballots were added in King County after election workers, under the close watch of party observers, "enhanced" ballots to reflect voters' intentions. Those could include, for example, ballots on which a voter circled the candidate's name, rather than filling in the oval for an optical scanning machine to read.