Estimating price elasticity of demand for electric vehicle charging contributes to the accurate determination of charging price, thereby improving electric vehicle adoption and energy sustainability. However, few studies have studied the impact of electricity price on electric vehicle charging behavior, especially the demand spillover effect caused by price fluctuations. To fill the gaps, on a citywide dataset of public charging piles in Shenzhen, China, first, correlation coefficients and hypothesis tests are used to determine the relationship between charging demand and price. A learning model incorporating two-layer graph attention, temporal pattern attention, and knowledge-embedded meta-learning is developed for accurate spatio-temporal regression. Impulse response analysis is conducted to unravel several noteworthy phenomena: (1) public charging demand is inelastic to electricity price, with an average elasticity of −0.76, and distinction between different functional areas and times is revealed; (2) negative price impulses marginally change the elasticity, while positive ones make electric vehicle charging users more price sensitive, and (3) the spillover effects caused by price increases and decreases bring 89.48% and 53.88% of its local demand changes to neighbors, respectively, with a scope of 3.45 kilometer. These findings provide policy implications for promoting electric vehicle charging to facilitate renewable energy transition.