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Peer assessment, as a form of collaborative learning, can engage students in active learning and improve their learning gains. However, current teaching platforms and programming environments provide little support to integrate peer assessment for in-class programming exercises. We identified challenges in conducting such exercises and adopting peer assessment through formative interviews with instructors of introductory programming courses. To address these challenges, we introduce PuzzleMe, a tool to help Computer Science instructors to conduct engaging in-class programming exercises. PuzzleMe leverages peer assessment to support a collaboration model where students provide timely feedback on their peers' work. We propose two assessment techniques tailored to in-class programming exercises: live peer testing and live peer code review. Live peer testing can improve students' code robustness by allowing them to create and share lightweight tests with peers. Live peer code review can improve code understanding by intelligently grouping students to maximize meaningful code reviews. A two-week deployment study revealed that PuzzleMe encourages students to write useful test cases, identify code problems, correct misunderstandings, and learn a diverse set of problem-solving approaches from peers.