Applications of spatial observations with excessive zeros occur in many disciplines. Modeling such zero-inflated spatial data is computationally challenging, especially in high dimensions. The computational challenge is borne out of inferring the high-dimensional spatial random effects. Also, Markov chain Monte Carlo (MCMC) algorithms may be slow mixing for these models. Here, we propose a computationally efficient approach to model high-dimensional zero-inflated spatial observations using a reduced-dimensional method based on random projections. Our approach improves mixing in MCMC algorithms, and also considerably reduces computational costs. Through simulated examples, we show that our approach performs well in inference and prediction. We also apply our approach to real world examples in ecology and glaciology.