WASHINGTON — The Senate approved the most fundamental alteration of its rules in more than a generation on Thursday, ending the minority party’s ability to filibuster most presidential nominees in response to the partisan gridlock that has plagued Congress for much of the Obama administration.

Furious Republicans accused Democrats of a power grab, warning them that they would deeply regret their action if they lost control of the Senate next year and the White House in years to come. Invoking the Founding Fathers and the meaning of the Constitution, Republicans said Democrats were trampling the minority rights the framers intended to protect. But when the vote was called, Senator Harry Reid, the majority leader who was initially reluctant to force the issue, prevailed 52 to 48.

Under the change, the Senate will be able to cut off debate on executive and judicial branch nominees with a simple majority rather than rounding up a supermajority of 60 votes. The new precedent established by the Senate on Thursday does not apply to Supreme Court nominations or legislation itself.

It represented the culmination of years of frustration over what Democrats denounced as a Republican campaign to stall the machinery of Congress, stymie President Obama’s agenda and block his choices for cabinet posts and federal judgeships by insisting that virtually everything the Senate approves be done by a supermajority.