SARS-CoV-2 has caused a global pandemic with significant humanity and economic loss since 2020. Currently, only limited options are available to treat SARS-CoV-2 infections for vulnerable populations. In this study, we report a universal fluorescence polarization (FP)-based high throughput screening (HTS) assay for SAM-dependent viral methyltransferases (MTases), using a fluorescent SAM-analogue, FL-NAH. We performed the assay against a reference MTase, NSP14, an essential enzyme for SARS-CoV-2 to methylate the N7 position of viral 5’-RNA guanine cap. The assay is universal and suitable for any SAM-dependent viral MTases such as the SARS-CoV-2 NSP16/NSP10 MTase complex and the NS5 MTase of Zika virus (ZIKV). Pilot screening demonstrated that the HTS assay was very robust and identified two candidate inhibitors, NSC 111552 and 288387. The two compounds inhibited the FL-NAH binding to the NSP14 MTase with low micromolar IC50. We used three functional MTase assays to unambiguously verified the inhibitory potency of these molecules for the NSP14 N7-MTase function. Binding studies indicated that these molecules are bound directly to the NSP14 MTase with similar low micromolar affinity. Moreover, we further demonstrated that these molecules significantly inhibited the SARS-CoV-2 replication in cell-based assays at concentrations not causing cytotoxicity. Furthermore, NSC111552 significantly synergized with known SARS-CoV-2 drugs including nirmatrelvir and remdesivir. Finally, docking suggested that these molecules bind specifically to the SAM-binding site on the NSP14 MTase. Overall, these molecules represent novel and promising candidates to further develop broad-spectrum inhibitors for the management of viral infections.