Generative AI, particularly Large Language Models (LLMs), can expand access to expert guidance in domains like education, where such support is often limited. We introduce Tutor CoPilot, a Human-AI system that models expert thinking to assist tutors in real time. In a randomized controlled trial involving more than 700 tutors and 1,000 students from underserved communities, students with tutors using Tutor CoPilot were 4 percentage points more likely to master math topics (p<0.01). Gains were highest for students of lower-rated tutors (+9 p.p.), and the tool is low-cost (about $20/tutor/year). Analysis of over 350,000 messages shows Tutor CoPilot promotes effective pedagogy, increasing the use of probing questions and reducing generic praise. In this work we show the potential for human-AI systems to scale expertise in a real-world domain, bridge gaps in skills, and create a future where high-quality education is accessible to all students.