We study how AI tutoring affects learning in higher education through a randomized experiment with 334 university students preparing for an incentivized exam. Students either received only textbook material, restricted access to an AI tutor requiring initial independent reading, or unrestricted access throughout the study period. AI tutor access raises test performance by 0.23 standard deviations relative to control. Surprisingly, unrestricted access significantly outperforms restricted access by 0.21 standard deviations, contradicting concerns about premature AI reliance. Behavioral analysis reveals that unrestricted access fosters gradual integration of AI support, while restricted access induces intensive bursts of prompting that disrupt learning flow. Benefits are heterogeneous: AI tutors prove most effective for students with lower baseline knowledge and stronger self-regulation skills, suggesting that seamless AI integration enhances learning when students can strategically combine independent study with targeted support.