Inslee stopped short of declaring victory over Republican Rob McKenna, acknowledging that the election's final result may not be known until the end of this week. Inslee held a promising advantage after more than 2 million votes were counted through Wednesday, carrying 51 percent of ballots.
Sensing a potential win, he began setting up a transition team that would help him prepare to take office in January.
"I'm just getting ready to lead the state of Washington," Inslee said.
Election officials estimate that hundreds of thousands of votes remain to be counted, with additional updates expected to be released Thursday afternoon and evening.
McKenna told supporters in a video message that he believed late ballots would break in his direction.
"We believe that my advantage among later voters is what is ultimately going to carry me to victory in this election," McKenna said. But after another day of counting, the results Wednesday were almost identical to those released Tuesday.
Washington is used to close governor's races. Most notably, Gov. Chris Gregoire won the 2004 contest by a mere 133 votes after two recounts and a court challenge.
Inslee's lead headlined broad victories for Democrats in Washington. The party easily kept control of a contested U.S. Senate seat while adding a new seat in the U.S. House. At the state level, they trailed in only one statewide race - secretary of state - but even that contest was too close to call.
On Wednesday, the Democrats seized control of the attorney general's office, which McKenna now leads.
Democrats also had endorsed a plan to legalize marijuana for recreational use, which passed, and a gay marriage measure, which was leading.
Republicans had hoped McKenna would provide fresh strength to a party that had gone 30 years without winning the governor's seat. Both sides poured millions of dollars into the race and polls had shown the candidates running about even.
McKenna built a moderate campaign platform around ways to increase funding for education, and he won the endorsement of 11 out of the 12 daily newspapers in the state along with some Democrats such as popular State Auditor Brian Sonntag. McKenna has worked the past eight years as the state's attorney general.
Inslee, a former congressman, first ran for governor in 1996 but lost to eventual Gov. Gary Locke. He focused his message on ways to grow the economy, vowing to focus state investments in certain industries, such as clean energy and life sciences.
Both candidates have vowed not to raise taxes.
Voters again made clear this year that they opposed taxes, re-approving a measure that requires lawmakers to have a two-thirds majority in order to raise taxes. And in two advisory votes, voters disapproved of efforts that increased taxes, including a proposal passed by the Legislature that repealed a tax exemption for out-of-state banks.