Sequential recommendation is essential in modern recommender systems, aiming to predict the next item a user may interact with based on their historical behaviors. However, real-world scenarios are often dynamic and subject to shifts in user interests. Conventional sequential recommendation models are typically trained on static historical data, limiting their ability to adapt to such shifts and resulting in significant performance degradation during testing. Recently, Test-Time Training (TTT) has emerged as a promising paradigm, enabling pre-trained models to dynamically adapt to test data by leveraging unlabeled examples during testing. However, applying TTT to effectively track and address user interest shifts in recommender systems remains an open and challenging problem. Key challenges include how to capture temporal information effectively and explicitly identifying shifts in user interests during the testing phase. To address these issues, we propose T$^2$ARec, a novel model leveraging state space model for TTT by introducing two Test-Time Alignment modules tailored for sequential recommendation, effectively capturing the distribution shifts in user interest patterns over time. Specifically, T$^2$ARec aligns absolute time intervals with model-adaptive learning intervals to capture temporal dynamics and introduce an interest state alignment mechanism to effectively and explicitly identify the user interest shifts with theoretical guarantees. These two alignment modules enable efficient and incremental updates to model parameters in a self-supervised manner during testing, enhancing predictions for online recommendation. Extensive evaluations on three benchmark datasets demonstrate that T$^2$ARec achieves state-of-the-art performance and robustly mitigates the challenges posed by user interest shifts.