The vote was 19-17, with Democrats unanimously voting no.
Had one more Republican joined them, the measure would have failed in what would have been a damaging, embarrassing, but not fatal, blow to the measure.
The legislation has the backing of President Donald Trump, who one lawmaker said called Republicans on the panel to press them to push the bill forward.
The committee debate a slew of non-binding proposals suggesting changes in the measure, with some expected from Republicans.
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The White House and Republican leaders are already talking to rank-and-file Republicans about revising the bill to nail down support.
Before the vote, panel Chairwoman Diane Black, R-Tenn., appealed to fellow Republicans to back the legislation, calling it "the conservative health care vision we've been talking about for years."
The measure would strike down much of former President Barack Obama's 2010 overhaul and reduce the federal role, including financing, for health care consumers.
Three members of the hard-line conservative House Freedom Caucus Representatives Dave Brat of Virginia, Gary Palmer of Alabama and Mark Sanford of South Carolina opposed the measure.
Democrats said the legislation would strip coverage from millions who gained it under Obama's 2010 overhaul and bestow a massive gift on the wealthy by repealing many of that law's tax increases.