Although counter-intuitive features have been observed in non-Hermitian optical systems based on micrometre-sized cavities, the achievement of a simplified but unambiguous approach to enable the efficient access of exceptional points (EPs) and the phase transition to desired lasing modes remains a challenge, particularly in wavelength-scale coupled cavities. Here, we demonstrate coupled photonic-crystal (PhC) nanolasers with asymmetric optical gains, and observe the phase transition of lasing modes at EPs through tuning of the area of graphene cover on one PhC cavity and systematic scanning photoluminescence measurements. As the gain contrast between the two identical PhC cavities exceeds the intercavity coupling, the phase transition occurs from the bonding/anti-bonding lasing modes to the single-amplifying lasing mode, which is confirmed by the experimental measurement of the mode images and the theoretical modelling of coupled cavities with asymmetric gains. In addition, we demonstrate active tuning of EPs by controlling the optical loss of graphene through electrical gating.