Is it possible to heat up a vapour-liquid mixture until it entirely condenses into liquid?

I have just begun studying P-V diagrams for phase-changes and I noticed something interesting which I cannot adequately explain.

Suppose you have a saturated vapour-liquid mixture in a strong rigid container that cannot expand or contract. Now suppose you begin heating the vapour-liquid mixture. As you supply heat, the pressure and temperature of the vapour-liquid mixture will increase. Suppose as well that the initial pressure and specific volume of the mixture are located to the left of the critical point as seen in the diagram below:

As you add heat, the pressure increases until you get to $P_{final}$ at which point the fluid is no longer a vapour-liquid mixture but now entirely a liquid. This seems to mean that under constant volume conditions you can heat a saturated vapour-liquid mixture to condense the vapour in the mixture into a liquid. But this doesn’t make intuitive sense to me because as you add heat, the temperature of the mixture will increase and so the evaporation rate should increase.

From my understanding of saturated vapour-liquid mixtures at equilibrium, the condensation rate of the vapour is equal to the evaporation rate of the liquid and hence no net change occurs (i.e it is in equilibrium). But if we increase the temperature and pressure of the mixture by adding heat, then the evaporation rate should increase along with the condensation rate (because the condensation rate is proportional to the pressure) meaning the amount of vapour present should neither increase nor decrease. Yet the diagram indicates that the amount of condensation in the process definitely exceeds the amount of evaporation in the process because the amount of vapour present in the mixture decreases to zero. So how is this possible? How can heating a liquid-vapour mixture cause the vapour within to condense?

Any help on this issue would be most appreciated!