Early viral infection is a race between spread and interferon (IFN) defense. Using spatial models, we show that noise asymmetrically shapes this race: stochastic viral bursts accelerate spread, while precise IFN timing improves containment. However, once secretion begins, fast, noisy release benefits both. We further show that infection outcome depends critically on how later immune cells are recruited—either by time or by cell count—fundamentally altering which parameters control viral control versus escape.