Emotional Support Conversation (ESC) aims to alleviate users’ emotional distress through multi-turn interactions by selecting appropriate support strategies and generating aligned responses. Despite recent progress, existing approaches face three key limitations: (1) the inability to capture sequential transition patterns of strategies within conversations; (2) a training-inference mismatch in strategy prediction; and (3) reliance on a shared decoder that limits strategy-specific expression. To address these challenges, we propose S3-ESC, a simple framework of three components that are model-agnostic across encoder-decoder ESC backbones. First, we introduce a Sequential strategy predictor that models strategy transition patterns. Second, we apply Scheduled sampling for strategy to mitigate the training-inference mismatch. Third, we propose Selective LoRA for strategy that enables strategy-specialized generation. Experiments on six ESC backbones show that S3-ESC consistently improves strategy prediction accuracy, by up to 4.5pp, while enhancing response quality on most of them. Our code is publicly available.