Novice students in law courses or students who encounter legal education face the challenge of acquiring specialized and highly concept-oriented knowledge. Structured and persuasive writing combined with the necessary domain knowledge is challenging for many learners. Recent advances in machine learning (ML) have shown the potential to support learners in complex writing tasks. To test the effects of ML-based support on students' legal writing skills, we developed the intelligent writing support system LegalWriter. We evaluated the system's effectiveness with 62 students. We showed that students who received intelligent writing support based on their errors wrote more structured and persuasive case solutions with a better quality of legal writing than the current benchmark. At the same time, our results demonstrated the positive effects on the students' writing processes.