Appeals judges yesterday threw out the manslaughter conviction of a Brooklyn woman accused of smothering her newborn daughter moments after birth.

The ruling is a “tremendous relief” to Laura Sergio, 30, who faced a five-year prison term if her conviction was upheld, said her lawyer, Richard Mischel.

Sergio gave birth April 6, 2007, to a baby girl in the Bay Ridge home she shared with her parents and two sisters. Someone then wrapped the baby in a towel and put her in a garbage bag.

The four-judge appellate panel said the evidence “did not eliminate the possibility” that someone else killed the child.