The SARS-CoV-2 beta coronavirus is spreading globally with unprecedented consequences for modern societies. The early detection of infected individuals is a pre-requisite for all strategies aiming to contain the virus. Currently, purification of RNA from patient samples followed by RT-PCR is the gold standard to assess the presence of this single-strand RNA virus. However, these procedures are time consuming, require continuous supply of specialized reagents, and are prohibitively expensive in resource-poor settings. Here, we report an improved nucleic-acid-based approach to detect SARS-CoV-2, which alleviates the need to purify RNA, reduces handling steps, minimizes costs, and allows evaluation by non-specialized equipment. The use of unprocessed swap samples and the ability to detect as little as three viral genome equivalents is enabled by employing a heat-stable RNA- and DNA-dependent DNA polymerase, which performs the double task of stringent reverse transcription of RNA at elevated temperatures as well as PCR amplification of a SARS-CoV-2 specific target gene. As results are obtained within 2 hours and can be read-out by a hand-held LED-screen, this novel protocol will be of particular importance for large-scale virus surveillance in economically constrained settings.