The Senate is expected to pass the bill later in the day. Friday's vote came days after Northeast Republicans erupted over House Speaker John Boehner's decision to delay an earlier vote.
The flood insurance measure is the first phase of a proposed Sandy aid package.
The House is set to vote on an additional $51 billion in recovery money on Jan. 15. Senate action on that measure is expected the following week.
The Associated Press contributed to this report.
