LLM-based search agents demonstrate strong capabilities in long-horizon information seeking and reasoning, typically trained via reinforcement learning. However, existing approaches predominantly rely on trajectory-level outcome rewards, providing limited supervision for complex search and reasoning processes. Although step-level credit assignment offers a promising solution, obtaining reliable and task-grounded supervision for open-ended search remains challenging. In this paper, we propose Evidence-Guided Group Relative Policy Optimization (EG-GRPO), a framework that derives step-level supervision from the evidence annotations available in synthetic deep search data. EG-GRPO identifies the first supporting citation for each required evidence claim and uses the newly acquired evidence to construct step-level process rewards. By representing the accumulated evidence as an evolving knowledge state, EG-GRPO further performs state-conditioned relative advantage estimation and combines the resulting step-level signal with the standard trajectory-level outcome advantage. Experiments on five challenging deep search benchmarks show that EG-GRPO generally outperforms standard GRPO and existing reward-enhanced and step-level RL baselines across different model scales. These results demonstrate that task-grounded evidence annotations can provide effective process supervision for credit assignment in deep search RL.

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