Video Large Language Models (Video-LLMs) have achieved strong performance on many video understanding tasks, yet remain vulnerable to temporal hallucination in time-sensitive reasoning scenarios such as scene transition understanding and event ordering. Existing solutions either require costly retraining or introduce inefficient multi-pass inference and external supervision at test time. In this work, we show that temporal evidence is already encoded in Video-LLM hidden representations but is not fully exploited during standard inference. Motivated by this observation, we propose Single-Pass Orthogonal Decomposition (SPOD), a training-free framework that recovers suppressed temporal evidence through analytical hidden-state manipulation in a single forward pass. SPOD consists of two components: Frame Distinctiveness Analysis (FDA), which identifies salient frames from middle-layer hidden-state geometry, and Temporal Delta Subspace (TDS), which constructs orthogonal temporal and prior subspaces from weighted inter-frame hidden-state differences. By decomposing final hidden states into temporal, prior, and residual components and rescaling them independently, SPOD enhances dynamic information, suppresses static appearance bias, and preserves complementary information. Experiments on VidHalluc, EventHallusion, and VideoMMMU show that SPOD consistently outperforms strong inference-time baselines across temporal reasoning tasks and model architectures while retaining near-vanilla inference efficiency. These results suggest that improving temporal reasoning in Video-LLMs may depend not only on additional supervision, but also on recovering temporal evidence already present in their internal representations. Our code is available at https://github.com/VioAgnes/SPOD.

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