Modern LLM serving systems must sustain high throughput while meeting strict latency SLOs across two distinct inference phases: compute-intensive prefill and memory-bound decode phases. Existing approaches either (1) aggregate both phases on shared GPUs, leading to interference between prefill and decode phases, which degrades Time-Between-Tokens (TBT); or (2) disaggregate the two phases across GPUs, improving latency but wasting resources through duplicated models and KV cache transfers. We present DuetServe, a unified LLM serving framework that achieves disaggregation-level isolation within a single GPU. DuetServe operates in aggregated mode by default and dynamically activates SM-level GPU spatial multiplexing when TBT degradation is predicted. Its key idea is to decouple prefill and decode execution only when needed through fine-grained, adaptive SM partitioning that provides phase isolation only when contention threatens latency service level objectives. DuetServe integrates (1) an attention-aware roofline model to forecast iteration latency, (2) a partitioning optimizer that selects the optimal SM split to maximize throughput under TBT constraints, and (3) an interruption-free execution engine that eliminates CPU-GPU synchronization overhead. Evaluations show that DuetServe improves total throughput by up to 1.3x while maintaining low generation latency compared to state-of-the-art frameworks.