In addition to the more detailed quoted answer, I believe the surviving mammals mostly lived underground, shielding them from many of the worst effects happenin

In addition to the more detailed quoted answer, I believe the surviving mammals mostly lived underground, shielding them from many of the worst effects happening on surface world. Many were blind anyway and did well in the darkness of the clouded surface. Their predators all died off. The biggest remaining threat would have been lack of food, but as the other answer states, they had more flexible diets than dinosaurs and mammals that did not survive.