Sen. Mike Lee, R-Utah, was the only Republican to oppose the bill but for a different reason than the 17 Democrats who fought for a lower rate.
Lee argues that the compromise just papers over the cracks in a fundamentally broken system.
"We should be working to create a higher education system that doesn't force students tens of thousands of dollars into debt in the first place, rather than fighting over $7 a month," Lee said in a statement.
The Senate legislation, he said, "doesn't come close to solving any problems."
Lee's most recent personal financial disclosure shows as of last year he had outstanding student loans of between $10,000 and $15,000, dating to 1997. The legislation on future rates would have no effect on his personal situation.
Hatch said he supported the bill because it "keeps student loan rates low for all federal loan beneficiaries," and he blamed Democrats for dragging out the debate with attempts to force an even lower rate.
"If it weren't for the obstructionism from Senate Democrats, this issue could have been solved earlier," Hatch said in a statement, pointing out that congressional Republicans were largely in agreement with President Barack Obama on this issue.
The president wanted three things: tie the interest rates to the rather stable Treasury notes, have one rate last for the life of the loan and have a cap so the rate wouldn't rise too high.
The Senate bill does so, tracking the rate to the high-yield 10-year Treasury note and allowing it to rise depending on the level of school. Undergraduates with subsidized and unsubsidized loans would pay 3.9 percent for loans taken out this summer. Graduate unsubsidized loans would be available at 5.4 percent. The higher interest PLUS loans would be at 6.4 percent.
While these rates may rise over time, the bill would be capped at 8.25 percent, 9.5 percent and 10.5 percent, respectively.
The bill is similar to one the House passed earlier this year.
The Senate vote was preceded by a standing ovation for Hatch to mark his 13,000th vote during his 37-year career as a lawmaker.