Ms Palin had claimed the newspaper defamed her by linking her to a 2011 shooting that left people dead and a US representative wounded.
The judge, however, has said he will allow the jury to deliberate a verdict in the case before it is thrown out.
Ms Palin is expected to appeal.
She originally filed her lawsuit against the newspaper in 2017, arguing her reputation was damaged by an opinion piece - written by its editorial board - which said her political rhetoric helped incite the 2011 shooting in Arizona that severely wounded US Representative Gabby Giffords and killed six other people.
The New York Times piece also said Ms Palin's political action committee had circulated a map of electoral districts that put Ms Giffords and 19 other Democrats under "stylised crosshairs".
Read More (...)