The 14 passengers aboard the overcrowded motorboat that capsized in New York Harbor were celebrating a birthday before it flipped off Liberty Island late Saturday, killing a mom and her infant daughter.

The 22-foot bowrider was chartered with “Zeus Luxury” for passenger Paula Rivera’s surprise 41st birthday on Saturday before the fatal accident unfolded, her daughter, Sara Raez, told The Post.

The group of family and friends boarded the boat at Randall’s Island around 7 p.m. for what was meant to be a memorable sightseeing voyage around the Statue of Liberty.

Just hours later, the boat — which was dangerously overcrowded — capsized, killing…

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