A novel hybrid maize variety designated 35Y33 and seed, plants and plant parts thereof, produced by crossing two Pioneer Hi-Bred International, Inc. proprietary inbred maize lines. Methods for producing a maize plant that comprises crossing hybrid maize variety 35Y33 with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into 35Y33 through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. This invention relates to the hybrid seed 35Y33, the hybrid plant produced from the seed, and variants, mutants, and trivial modifications of hybrid 35Y33. This invention further relates to methods for producing maize lines derived from hybrid maize variety 35Y33 and to the maize lines derived by the use of those methods.