The four-year civil war has killed more than 10,000 people, mostly civilians, displaced 3 million others, and pushed the country to the brink of starvation. The Trump administration declined to certify last month that the Saudis were undertaking efforts to reduce civilian casualties despite a congressional mandate do so as a condition for resuming U.S. assistance.
Trump has threatened to veto the bill if it reaches his desk, saying it would undermine the counterterrorism fight.
But the resolution will probably be struck down by Mr Trump's first veto since he took office.
Change in the U.S. -Saudi relationship is obviously due in large part to the murder of Washington Post columnist Jamal Khashoggi, which the Central Intelligence Agency concluded with high confidence was ordered by Saudi Crown Prince Mohammed bin Salman.
The seven Republicans who defied the President aligned with the Democrats.
The United States provides weapons and refueling to the Saudi coalition.
The text now heads to the Democrat-led House of Representatives, which approved a similar measure that stalled earlier this year, and which is likely to pass the latest effort.
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"Today, we begin the process of reclaiming our constitutional power by ending USA involvement in a war that has not been authorized by Congress and is clearly unconstitutional", Senator Bernie Sanders, who is a presidential candidature for the 2020 elections, said on the Senate floor.
The Senate has passed "war powers" legislation ordering the president to cease and desist his cooperation with Saudi Arabia in the destruction of Yemen.
The measure was put to vote under the War Powers Act, which allows the resolution to be fast-tracked through US Congress.
"We should not use this specific vote on a specific policy decision as some proxy for all the Senate's broad feelings about foreign affairs".
The resolution passed by 54 votes to 46 and called to "direct the removal of US Armed Forces from hostilities in the Republic of Yemen that have not been authorised by Congress".
Democratic Senator Chris Murphy of CT hailed the outcome.
In that case too, he has promised to use his veto.
Hours ahead of the vote, the White House statement threatening a veto argued that USA support for the Saudis does not constitute engaging in "hostilities" and that the resolution could undermine the fight against violent extremism.
Coalition forces led by Saudi Arabia and the United Arab Emirates have relentlessly bombed Yemen since 2015 in an effort to oust the Houthi rebels controlling the capital city of Sana'a.