Introduction: This cross-sectional study evaluated the impact of socioeconomic status on the knowledge, attitudes, and practices (KAP) concerning zoonotic visceral leishmaniasis (VL) among dog owners from the municipality of Rondonópolis—a highly endemic area for the disease in Central-Western Brazil. Methodology: Data were collected between 2016 and 2017 during a household survey. A probabilistic sample of 404 dog owners were interviewed assessing sociodemographic characteristics, previous occurrence of VL cases, and KAP about human VL, vector, and canine VL. Responses regarding KAP were compared among social classes, which are indicators of socioeconomic status. Correct/appropriate answers were scored, and a multivariate Poisson regression analysis evaluated the impact of social class on scoring. Results: The overall KAP regarding VL was limited. Dog owners from higher social classes differed from those of the lower classes regarding the recognition of abdominal distension (p = 0.026) and skin lesions (p < 0.001) as clinical manifestations of human and canine VL, respectively, knowledge of VL transmission (p = 0.020), use of topical repellents (p < 0.001), use of insecticide-impregnated collars (p = 0.003), and previous attempts of treatment for canine VL (p = 0.005). Higher scores were associated with the upper social classes (IRR = 1.18; CI = 1.08-1.29) adjusted by the age (IRR = 1.13; CI = 1.04-1.24) and the previous occurrence of human (IRR = 1.21; CI = 1.07-1.36) and canine (IRR = 1.25; CI = 1.14-1.36) VL in the household/neighbourhood of the respondents. Conclusions: Improved KAP concerning VL was associated with better socioeconomic status of dog owners.