Emotional Support Conversation aims at reducing the seeker's emotional distress through supportive response. Existing approaches have two limitations: (1) They ignore the emotion causes of the distress, which is important for fine-grained emotion understanding; (2) They focus on the seeker's own mental state rather than the emotional dynamics during interaction between speakers. To address these issues, we propose a novel framework CauESC, which firstly recognizes the emotion causes of the distress, as well as the emotion effects triggered by the causes, and then understands each strategy of verbal grooming independently and integrates them skillfully. Experimental results on the benchmark dataset demonstrate the effectiveness of our approach and show the benefits of emotion understanding from cause to effect and independent-integrated strategy modeling.