The vote – called “cloture” – was a test of support for the embattled nominee who has faced sexual assault allegations from several women.
All eyes are on four swing senators for Saturday’s final vote.
Cloture passed with 51 in favour. Republicans have a 51-49 majority.
One of the key swing votes, Senator Lisa Murkowski, voted against advancing Mr Kavanaugh.
Mr Kavanaugh’s confirmation in the final vote on Saturday would tilt the country’s top court in favour of conservatives for years to come.
The nine-member panel has the final say on issues such as abortion, gun control and voting rules and justices are appointed for life.
As the senate began its deliberations on Friday morning, the party divisions were laid bare in the opening remarks from representatives of both parties.