MPs rejected a bid by the opposition Conservatives to refer the prime minister to the Commons Privileges Committee on Tuesday by 335 to 223 after Labour MPs were ordered to oppose the move.
Conservative leader Kemi Badenoch had accused Starmer of misleading the parliament by claiming "full due process" had been followed and "no pressure existed" in Mandelson's appointment.
Some Labour figures have branded Badenoch's call for an investigation a "political stunt".
But a handful of Labour backbenchers broke ranks on Tuesday to criticise the government for whipping its MPs to oppose the motion, and suggested the prime minister should refer himself to the Privileges Committee to "clear his name".
Fifteen Labour MPs rebelled against the whip and backed Badenoch's motion, along with Hull MP Karl Turner who recently lost the Labour whip over his opposition to plans to limit jury trials.
Starmer himself attended the Commons on Tuesday evening to vote against the motion.
Following the vote, a Downing Street spokesman said the government was "delivering for Britain" while the Conservatives had "resorted to this desperate political stunt" ahead of local elections "because they have no answers on the cost of living or the NHS".
Badenoch said Labour MPs would "rue the day" they voted against the motion, accusing them of being "complicit" in a "cover-up".
"This is a government coming apart at the seams," Badenoch said.
"They are more interested in their own survival than the cost-of-living crisis affecting hardworking families."
Liberal Democrat leader Ed Davey said Starmer had "ducked scrutiny" by whipping his MPs to oppose the Conservative motion, describing the move as "cowardly".
Starmer has consistently denied misleading the House, leaning on the conclusion of former cabinet secretary Chris Wormald that "appropriate processes" were followed.
But earlier on Tuesday, former senior Foreign Office mandarin Philip Barton declined to endorse Starmer's assessment, saying it was for MPs to form their own view.
Barton told the Commons Foreign Affairs Committee it was unusual for the peer's appointment to be announced before security vetting had been completed and suggested there was pressure to "get on with" approving Mandelson's developed vetting.
The committee also heard from Starmer's former chief of staff Morgan McSweeney, who insisted he did not "ask officials to ignore procedures, request that steps should be skipped, or communicate explicitly or implicitly that checks should be cleared at all costs" during the appointment of Mandelson.
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