This invention relates to separators for batteries and other electrochemical cells, especially lithium-ion batteries, having a shutdown mechanism. The separator is a laminate that contains a nonwoven nanoweb and a porous layer composed of a plurality of thermoplastic particles having particle size smaller than the mean flow pore size of the nanoweb. The shutdown layer melts and starts to flow at a desired temperature, and restricts the ion flow path, resulting in a substantial decrease in ionic conductivity of the separator at the desired shutdown temperature, while leaving the separator intact.