This study aims to examine the neural mechanisms of resolving response competition during bilingual word recognition in the context of language intermixing. During fMRI scanning, Chinese–Japanese unbalanced bilinguals were required to perform a second-language (L2) lexical decision task composed of cognates, interlingual homographs, matched control words from both Chinese (first language) and Japanese (L2), and pseudowords. Cognate word processing showed longer reaction times and greater activation in the supplementary motor area (SMA) than L2 control word processing. In light of the orthographic and semantic overlap of cognates, these results reflect the cognitive processing involved in resolving response conflicts enhanced by the language membership of non-target language during bilingual word recognition. A significant effect of L2 proficiency was also observed only in the SMA, which is associated with the task decision system. This finding supports the bottom-up process in the BIA+ model and the Multilink model. The task/decision system receives the information from the word identification system, making appropriate responses during bilingual word recognition.