In a 66 to 34 vote, senators moved toward confirming her as the next attorney general.
The Senate leader said the bill will be "open for amendment."
The Senate could take a final vote on Loretta Lynch's nomination Thursday.
But senators rejected an amendment she was pressing for them to adopt.
Paul gave a fist-bump to Harry Reid on the Senate floor.
Obama's long-delayed nominee for attorney general could get a final vote as soon as Thursday.
Senate Majority Leader Mitch McConnell touted the vote as a win for Republicans.
The amendment clears the way for passage of an anti-human-trafficking bill.
Sanders said that there has not been "a lot of transparency" on TPP legislation.
The Senate is expected to vote on the legislation Wednesday.