Developmental dyslexia is often accompanied by altered phonological processing of speech. Underlying neural changes have typically been characterized in terms of stimulus- and/or task-related responses within individual brain regions or their functional connectivity. Less is known about potential changes in the more global functional organization of brain networks. Here we recorded electroencephalography (EEG) in typical and dyslexic readers while they listened to (a) a random sequence of syllables and (b) a series of tri-syllabic real words. The network topology of the phase synchronization of evoked cortical oscillations was investigated in four frequency bands (delta, theta, alpha and beta) using minimum spanning tree graphs. We found that, compared to syllable tracking, word tracking triggered a shift toward a more integrated network topology in the theta band in both groups. Importantly, this change was significantly stronger in the dyslexic readers, who also showed increased reliance on a right frontal cluster of electrodes for word tracking. The current findings point towards an altered effect of word-level processing on the functional brain network organization that may be associated with less efficient phonological and reading skills in dyslexia.