The vote in the Senate Foreign Relations Committee was 11 to 10, along strict party lines, setting up a period of debate and subsequent vote on an as-yet-undetermined day in the Republican-controlled Senate.
With just two of Trump's cabinet members in place -- Secretary of Defense James Mattis and Homeland Security Secretary John Kelly -- Senate Republicans have sought to speed up confirmation of his other nominees, including his choice to head the CIA.
The Senate was expected to confirm Mike Pompeo as head of the spy agency later Monday.
Tillerson received a major boost when Senator Marco Rubio, one of three Republicans who had expressed doubts about him, announced he will support Tillerson for the post despite serious reservations.
Rubio said he still had concerns about Tillerson's positions on human rights.
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But he stressed that given the "uncertainty" about the direction of US foreign policy, "it would be against our national interests to have this confirmation unnecessarily delayed or embroiled in controversy."
Senators John McCain and Lindsey Graham, the other Republicans who had expressed reservations about Tillerson and his past dealings with Russia, gave their blessing on Sunday.
Republicans hold 52 seats in the 100-seat Senate. A simple majority is required for confirmation of cabinet positions.
"I personally have no doubt that Rex Tillerson is well-qualified," said the committee's chairman, Senator Bob Corker.
'Demonstrated business orientation'
But the panel's Democrats voted in unison against Tillerson.
"I believe Mr Tillerson's demonstrated business orientation... could compromise his ability as secretary of state to forcefully promote the values and ideals that have defined our country and our leading role in the world for more than 200 years," Senator Ben Cardin said in a statement.
Trump's team had called for several nominees to be confirmed Friday on the day Trump was sworn in, but Democrats blocked votes, arguing that ethics reviews and other vetting of key nominees had been insufficient.
Former president Barack Obama had seven nominees approved on his first day as president in 2009.
Senate Majority Leader Mitch McConnell told Fox News Sunday that despite the delays by Democrats, "I believe we will be able to confirm the entire cabinet."
Republicans had hoped to push through Pompeo's confirmation Friday, but Democrats balked, arguing that a CIA director had never been put in place on Inauguration Day.
The delay drew criticism Saturday from Trump's press secretary Sean Spicer, who charged that Democrats were "playing politics with national security."
Republicans were also hoping to get Trump's pick for US attorney general, Senator Jeff Sessions, installed swiftly.
The Senate Judiciary Committee is scheduled to vote on Sessions on Tuesday, when the Foreign Relations Committee votes on South Carolina Governor Nikki Haley's nomination to be US ambassador to the United Nations.
