Early diagnosis with rapid detection of the virus plays a key role in preventing the spread of infection and in treating patients effectively. In order to address the need for a straightforward detection of SARS-CoV-2 infection and assessment of viral spread, we developed rapid, sensitive, extraction-free one-step reverse transcription-quantitative polymerase chain reaction (RT-qPCR) and reverse transcription loop-mediated isothermal amplification (RT-LAMP) tests for detecting SARS-CoV-2 in saliva. We analyzed over 700 matched pairs of saliva and nasopharyngeal swab (NSB) specimens from asymptomatic and symptomatic individuals. Saliva, as either an oral cavity swab or passive drool, was collected in an RNA stabilization buffer. The stabilized saliva specimens were heat-treated and directly analyzed without RNA extraction. The diagnostic sensitivity of saliva-based RT-qPCR was at least 95% in individuals with subclinical infection and outperformed RT-LAMP, which had at least 70% sensitivity when compared to NSBs analyzed with a clinical RT-qPCR test. The diagnostic sensitivity for passive drool saliva was higher than that of oral cavity swab specimens (95% and 87%, respectively). A rapid, sensitive one-step extraction-free RT-qPCR test for detecting SARS-CoV-2 in passive drool saliva is operationally simple and can be easily implemented using existing testing sites, thus allowing high-throughput, rapid, and repeated testing of large populations. Furthermore, saliva testing is adequate to detect individuals in an asymptomatic screening program and can help improve voluntary screening compliance for those individuals averse to various forms of nasal collections.