The SARS-CoV-2 replication and transcription complex (RTC) comprising nonstructural protein (nsp) 2-16 plays crucial roles in viral replication, reducing the efficacy of broad-spectrum nucleoside analog drugs such as remdesivir and in evading innate immune responses. Most studies target a specific viral component of the RTC such as the main protease or the RNA-dependent RNA polymerase. In contrast, our strategy is to target multiple conserved domains of the RTC to prevent SARS-CoV-2 genome replication and to create a high barrier to viral resistance or evasion of antiviral drugs. We show that clinically-safe Zn-ejector drugs, disulfiram/ebselen, can target conserved Zn2+-sites in SARS-CoV-2 nsp13 and nsp14 and inhibit nsp13 ATPase and nsp14 exoribonuclease activities. As the SARS-CoV-2 nsp14 domain targeted by disulfiram/ebselen is involved in RNA fidelity control, our strategy allows coupling of the Zn-ejector drug with a broad-spectrum nucleoside analog that would otherwise be excised by the nsp14 proofreading domain. As proof-of-concept, we show that disulfiram, when combined with remdesivir, can synergistically inhibit SARS-CoV-2 replication in Vero E6 cells. We present a mechanism of action and the advantages of our multi-targeting strategy, which can be applied to any type of coronavirus with conserved Zn2+-sites.