Virus-specific humoral and cellular immunity act synergistically to protect the host from viral infection. We interrogate the dynamic changes of virological and immunological parameters in 12 patients with symptomatic acute SARS-CoV-2 infection from disease onset to convalescence or death. We quantify SARS-CoV-2 viral RNA in the respiratory tract in parallel with antibodies and circulating T cells specific for various structural (nucleoprotein [NP], membrane [M], ORF3a, and spike) and non-structural (ORF7/8, NSP7, and NSP13) proteins. Although rapid induction and quantity of humoral responses associate with an increase in disease severity, early induction of interferon (IFN)-γ-secreting SARS-CoV-2-specific T cells is present in patients with mild disease and accelerated viral clearance. These findings provide support for the prognostic value of early functional SARS-CoV-2-specific T cells with important implications in vaccine design and immune monitoring.