Gout, the most prevalent inflammatory arthritis, is becoming increasingly prevalent in the United States and across the world, and it adversely impacts people’s quality of life and their health. Few studies have focused on the relationship between daily dietary quality and gout, so the topic requires further exploration. Data were derived from the National Health and Nutrition Examination Survey 2007–2016, and the inclusion criteria of the analytic sample were (1) adults, age ≥20 years, with complete information about HEI-2015, gout, and uric acid; (2) complete information of demographics, lifestyle (BMI, smoking, drinking), and disease history [hypertension, chronic kidney disease (CKD), diabetes]. The quality of the daily diet was reflected using the Healthy Eating Index 2015 (HEI-2015). The baseline features of different groups were examined using the Scott-Rao chi-square tests, and the association between the HEI-2015 score and the risk of gout/hyperuricemia (HUA) was investigated using weighted logistic regression models. The effects of different dietary components in the HEI-2015 on reducing the risk of gout/HUA were evaluated by weighted quantile sum (WQS) regression models. After adjusting for demographic characteristics, behavioral covariates, and disease history, higher HEI-2015 scores were associated with a significantly lower risk of gout (OR: 0.878, 95% CI: 0.876–0.880) and HUA (OR: 0.978, 95% CI: 0.976–0.979) in weighted logistic regression. Dairy, whole grains, plant proteins, and added sugar contributed greatly in HEI-2015 to reducing gout risk (weights of WQS index: 42, 17.18, 16.13, and 7.93%, respectively). Dairy, total fruits, greens and beans, and plant proteins contributed greatly in HEI-2015 to reducing HUA risk (weights of WQS index: 28.9, 17.13, 16.84, and 11.39%, respectively). As the result, adherence to the American Dietary Guidelines may assist to decrease the risk of gout/HUA in American adults, and greater emphasis should be placed on dairy products, whole grains, fruits, legumes, and added sugars.