The vote was held after the government reached a compromise deal, giving coalition members freedom to vote as they want on the contested bill that would give ultra-Orthodox seminary students exemption from military conscription.
Some Israeli political commentators accuse Lieberman and Netanyahu of working together to preserve the option of fresh polls for the prime minister.
Efforts had intensified throughout the day to reach a deal to prevent early elections.
The prime minister on Monday attempted to shut down rumors that new elections are his way of garnering support ahead of a possible indictment on corruption charges, insisting that he has no desire to go to the polls.
They taunted Netanyahu, claiming that he engineered a crisis to try to force elections before the outcome of corruption investigations against him are known.
Helping to stave off the crisis, the 2019 state budget will be approved this week before the end of the winter session in line with demands of Finance Minister Moshe Kahlon who said he would step down from his post and pull his party from the coalition if it failed to pass.
Haaretz reported that Netanyahu did not have enough votes in the Knesset to bring down the government and trigger an early election.
Members of Netanyahu's government had been quarrelling over whether to extend military draft exemptions afforded to ultra-Orthodox men.
Netanyahu separately called on Lieberman and all other coalition partners to remain in the government.
Defense Minister Avigdor Liberman leads a faction meeting of his Yisrael Beytenu party at the Knesset
But while Netanyahu's future dominated the conversation, the resolution of the crisis hinged on separate, more technical issues.
On Wednesday, Regional Cooperation Minister Tzachi Hanegbi, a loyal Netanyahu ally, said "an accurate description would be to say that the prime minister was indifferent to the outcome".
Ultra-Orthodox parties form a central plank in Netanyahu's ruling coalition government, and the leader has aroused anger due to his acquiescence to the groups on a range of issues.
Lieberman meanwhile opposes the conscription legislation and wants to see the ultra-Orthodox serve in the military like their secular counterparts.
Landver will on Tuesday present her appeal against a decision to allow the Knesset to vote on the controversial bill to the Ministerial Committee for Legislation.
But, Lieberman said, "can elections still be prevented?" In the other, he is suspected of promoting regulation that would benefit an Israeli daily newspaper in exchange for more favorable coverage.
The country's attorney general is now examining whether to indict Netanyahu in two separate cases.
Four corruption investigations looking into his affairs have led to predictions of his eventual downfall after a total of 12 years as prime minister, first from 1996 to 1999, then again beginning in 2009.
But since Netanyahu is not legally required to resign if indicted, his fate may be far from sealed even if he is charged.