It split along party lines, with all 11 Republicans voting in favor and all 10 Democrats against. A full vote will now be held in the Republican-run Senate.
The move capped a busy day for the new Donald Trump administration.
Most notable was the US withdrawal from the Trans-Pacific Partnership, fulfilling a campaign pledge.
President Trump signed an executive order to pull out of the 12-nation trade deal that had been a linchpin of former President Barack Obama’s Asia policy.
“Great thing for the American worker what we just did,” Mr. Trump said.
Also on Monday, the Senate confirmed Mike Pompeo as Mr. Trump’s CIA director.
Mr. Pompeo’s immediate task, correspondents say, will be to establish an effective relationship between the spy agency and Mr. Trump.
The president has been critical of the CIA for concluding that Russia had been actively working to influence the US presidential election in his favor.
In another development, new US Defence Secretary James Mattis said Washington had an “unshakeable commitment” to Nato, despite Mr. Trump’s earlier description of the military alliance as “obsolete”.
The Senate Foreign Relations Committee approved Mr. Tillerson after leading Republican Senator Marco Rubio dropped his opposition.
Mr. Rubio sparred with Mr. Tillerson, a 64-year-old Texan oil executive, during confirmation hearings earlier this month, accusing him of being soft on Russia.
The former head of Exxon Mobil, Mr. Tillerson knows Russian President Vladimir Putin through his business dealings