Rain-fed potato (Solanum tuberosum) fields in drylands significantly contribute to nitrous oxide (N2O) emissions, making them an important focus of agricultural greenhouse gas research. Film mulching and ridging are key agricultural methods in potato cultivation. Investigating the impact of these methods on N2O emissions, nitrifying/denitrifying functional genes, and microbial communities can provide a theoretical basis for soil emission reduction and more sustainable dryland agriculture. We examine the effects of flat tillage with mulching, ridge tillage with mulching, flat tillage without mulching, and ridge tillage without mulching, on potato fields under natural rainfall conditions in Wuchuan County, China. N2O emission fluxes were monitored using a static (dark) chamber and gas chromatography. Real-time quantitative PCR (q-PCR) was used to quantify abundances of nitrifying and denitrifying bacteria related to N2O emissions at various potato-growth stages. Illumina high-throughput sequencing was used to investigate microbial community structure by targeting 16S rRNA genes; related soil elements (soil temperatures and moisture) are analyzed. Mulching and ridging indirectly influence N2O emissions, nitrifying/denitrifying functional gene copy numbers, and microbial community structure by altering soil temperature and moisture. Cumulative N2O emissions and emission intensity were both consistently higher in ridge tillage with mulching during the potato-growing period. Ammonia-oxidizing archaea are the main microorganisms that control N2O emissions, with nitrification-coupled denitrification also being an important mechanism contributing to high N2O emissions during soil dry–wet cycles. Increased soil temperature and moisture elevated N2O emissions and functional gene copy numbers. The combination of mulching and ridging effectively uses the characteristics of both practices, making Nitrospira the dominant genus, and significantly increases N2O emissions.