The ability of bilingual individuals to manage two competing languages is assumed to rely on both domain-specific language control and domain-general control mechanisms. However, previous studies have reported mixed findings about the extent and nature of cross-domain generality. The present study examined the role of language dominance, along with bilingual language experience, in the relationship between word recognition and domain-general cognitive control. Two single-language lexical decision tasks (one in L1 and another in L2) and a domain-general flanker task were administered to bilinguals who live in the sociolinguistic context of a minority and a majority language, namely, Uyghur (L1) and Chinese (L2), respectively. The results showed a diversity in language dominance patterns with better performance in L2 than L1 in the recognition modality, even for participants who self-identified as globally being dominant in L1. This finding reflected all bilinguals’ self-evaluation that their preferred language for reading was L2, suggesting that language dominance is dynamic, depending on what language modality is measured. Furthermore, it was found that an earlier onset age of L2 acquisition (but not recent exposure) and a higher across-modality dominance in L2 were related to faster L2 word recognition. When self-reported language dominance was operationalised as a grouping variable, it was further found that both across-modality L1- and L2-dominant bilingual participants demonstrated a significant relationship between L2 word recognition and domain-general monitoring control, while only L1-dominant bilinguals additionally tapped into inhibitory control, indexed by the flanker effect during L2 word recognition. These findings suggest that language dominance has an impact on the extent and nature of the overlap in control mechanisms across specific linguistic and domain-general cognitive domains and add evidence to a domain-general monitoring account of bilingual word recognition.