Determining temporal similarity in shape between electromyographic (EMG) and center-of-pressure (COP) signals reflects neuromuscular control in terms of which relevant muscles are involved in maintaining balance. The current study aimed to investigate a cross-correlation between seven lower-limb EMG activities and COP displacements, simultaneously measured in 25 young adults unipedally balancing on stable and multiaxial-unstable surfaces. The effect of surface stability, sway direction, and leg dominance was then tested on two EMG–COP correlation levels: individual muscles and groups (patterns) of multi-muscles involved in postural sway, as determined by principal component analysis (PCA). The results show that two factors demonstrate their effects only at the level of individual muscles: sway direction (p ≤ 0.003) and leg dominance (p = 0.003). Specifically, the semitendinosus, tibialis anterior, peroneus longus, and soleus correlate more with the mediolateral postural sway than with the anteroposterior postural sway, except for the gastrocnemius medialis. Additionally, balancing on the non-dominant leg shows a lower correlation between the semitendinosus and postural sway than on the dominant leg. The current findings suggest that when achieving unipedal equilibrium, the postural control system may be constrained the most in the specific muscles of the least steady conditions, e.g., the frontal plane and non-preferred leg.