The 63-36 vote came after Republican opponents, apparently feeling political heat, abandoned their filibuster tactics and let the bill come to a vote without changes that they had insisted were nonnegotiable.
Sixteen Republicans joined 47 Democrats in favor of the bill, with 28 Republicans and eight Democrats voting against it. Maryland's two senators -- Barbara A. Mikulski and Paul S. Sarbanes, both Democrats -- voted in favor of the bill.
The resurrection of the bill was surprising because it had been declared dead for this year after its advocates failed Friday to get the 60 votes needed to shut off debate. The bill now goes to a conference committee, to be reconciled with a version passed by the House.
It was unclear whether a compromise version will be ready for approval before Congress adjourns this week.
With congressional approval now virtually certain, the Senate action appears to set a landmark in the national debate over gun control. The Brady bill -- named for President Ronald Reagan's press secretary, James Brady, who was wounded in the 1981 assassination attempt on Mr. Reagan -- was viewed as a breakthrough for broader government action on gun ownership.
The passage also inflicted a major defeat on the influential gun lobby, which had fought to weaken or sidetrack the legislation. Lawmakers had seen polls indicating public support for the gun-control measure.
"It's been a long, difficult and, in its early years, lonely fight," said Senate Majority Leader George J. Mitchell, D-Maine, predicting that enactment is imminent "at long last."
Meanwhile, in a year-end burst of congressional activity yesterday:
* The Senate voted 54-45 for a $18.3 billion bill to finish the cleanup of failed savings and loan institutions. House approval is expected tomorrow.
* The Senate approved legislation to extend unemployment benefits for those who have exhausted them. The measure was sent to the House after lawmakers rejected, 63-36, an attempt by Sen. Phil Gramm, R-Texas, to insert a provision to lock in cuts in the federal work force that President Clinton favors.
* The House debated legislation to make the District of Columbia the 51st state. The measure is expected to fail in a vote scheduled for today.
* The Senate approved a bill repealing remaining U.S. economic sanctions imposed against South Africa because of its former racial policies and sent it on to Mr. Clinton for his signature.
* Mr. Clinton's plan to overhaul health care legislation was introduced in both the House, where it had 100 co-sponsors, and in the Senate, where it had 31.
The Brady bill requires stores to wait five days before releasing a handgun to a purchaser. It authorizes spending of $200 million a year for modernizing criminal records so that a computerized search can check for any criminal histories or indications of mental disorders of potential purchasers. Once the check system becomes instantaneous and operational nationally, the waiting period could be eliminated.