The legislation cleared a key hurdle on a 60-37 vote, precisely the number needed.
A final vote is expected by Wednesday on the House-passed measure, which would then go to the White House for Obama's signature.
It is one of several measures comprising Obama's second-term trade agenda as the administration works to finalize a 12-nation agreement among countries on both sides of the Pacific Ocean
Another bill, to provide federal aid to workers who lose their jobs because of imports, is also awaiting approval. The rescue plan hatched last week calls for the Senate to pass that measure and the House to follow suit later this week, just before lawmakers begin a July 4 vacation.
Eager to reassure Democrats who expressed doubt about a GOP commitment to pass the follow-up bill, Speaker John Boehner, R-Ohio, issued a statement saying the House will vote on it "once it passes the Senate."
The legislation has the support of the administration and business organizations, who say it is necessary to win lower barriers to U.S-made goods around the world.
Opponents include organized labor and most Democrats in Congress, who argue that past global trade deals have resulted in the large scale loss of American jobs — and claim this time would be no different.
Those differences were reflected on the Senate floor.
Majority Leader Mitch McConnell, R-Ky., said the vote demonstrated "we can work together on something that's important for our country."
But Sen. Sherrod Brown, D-Ohio, said it would be a "day of celebration in corporate suites."
The vote in the Senate was similar to an earlier roll call on the same legislation.
Republican Sen. Ted Cruz, a presidential hopeful, flipped his vote from support to opposition, saying it had become "enmeshed in corporate backroom deal making."
He did not say why he initially voted for it.
Democratic Sen. Ben Cardin of Maryland, voted against advancing the bill after supporting its passage on the earlier vote. His office provided no immediate explanation for the shift.
In all 47 Republicans and 13 Democrats joined forces to assure the bill's progress.
The negotiating authority that Obama seeks is known as "fast-track." Most recent presidents have said the same power. Without it, the bill's supporters say, other nations would be highly reluctant to make the type of compromises that are necessary to seal global trade deals, because they fear that Congress would demand additional concessions.
The week's maneuvering came a little less than two weeks after the House derailed the trade legislation in a revolt triggered by union-backed Democrats and supported by the party's leader, Rep. Nancy Pelosi of California.
Originally, the trade negotiating authority and program of aid for displaced workers were part of one bill, but subject to separate votes.
Democrats who normally support the aid turned against it in the House, and voted it down. That temporarily derailed the entire legislation, sending Obama, McConnell and Boehner scurrying to come up with a rescue plan.
The revised approach was to separate the trade bill from the aid measure, and rely on a strong Republican vote to pass one of them, and a strong Democratic show of support to approve the other.
Obama has said consistently he wants both measures to reach his desk, but House Democrats have not yet said if they will try to block the aid program as part of a desperate move to persuade Obama not to sign the trade bill he so eagerly seeks.
Nor has Obama said what he would do if only the trade bill passes, and the aid measure remains stuck because Democrats without support.