So in this scenario, we have to consider two things: the plants are super different from each other. Some plants have huge leaves, others have tiny ones-- some plants have really long roots, others barely have them; it is because of these differences that the some plants survive better than others.
Say that at the start, plants are thriving like crazy-- I mean they're everywhere man.
But afterwards, this huge environmental change occurs.
Plants that have bigger leaves lose more water due to a greater rate of transpiration. Plants with shorter roots can't reach the water deep in the soil.
Plants with smaller leaves, and waxier cuticles could protect their water more. Plants with longer roots could get more water.
Basically, all plants that have good traits for drier environments tend to survive more.
Because they tend to survive more-- they could make more baby plants (i.e. greater rate of reproduction)
Because they could make more baby plants, the overall newer generation of plants will have more of these hardy, dry-environment adapted plant traits (i.e. phenotype).