Effective speech sound discrimination at preschool age is known to be a prerequisite for the development of language skills and later literacy acquisition. However, the speech specificity of cortical discrimination skills in small children is currently not known, as previous research has either studied speech functions without comparison with non-speech sounds, or used much simpler sounds such as harmonic or sinusoidal tones as control stimuli. We investigated the cortical discrimination of five syllable features (consonant, vowel, vowel duration, fundamental frequency, and intensity), covering both segmental and prosodic phonetic changes, and their acoustically matched non-speech counterparts in 63 6-year-old typically developed children, by using a multi-feature mismatch negativity (MMN) paradigm. Each of the five investigated features elicited a unique pattern of differentiating negativities: an early differentiating negativity, MMN, and a late differentiating negativity. All five studied features showed speech-related enhancement of at least one of these responses, suggesting experience-related neural commitment in both phonetic and prosodic speech processing. In addition, the cognitive performance and language skills of the children were tested extensively. The speech-related neural enhancement was positively associated with the level of performance in several neurocognitive tasks, indicating a relationship between successful establishment of cortical memory traces for speech and enhanced cognitive functioning. The results contribute to the understanding of typical developmental trajectories of linguistic vs. non-linguistic auditory skills, and provide a reference for future studies investigating deficits in language-related disorders at preschool age.