A/B tests, also known as online controlled experiments, have been used at scale by data-driven enterprises to guide decisions and test innovative ideas. Meanwhile, non-stationarity, such as the time-of-day effect, can commonly arise in various business metrics. We show that inadequately addressing non-stationarity can cause A/B tests to be statistically inefficient or invalid, leading to wrong conclusions. To address these issues, we develop a new framework that provides appropriate modeling and adequate statistical analysis for non-stationary A/B tests. Without changing the infrastructure for any existing A/B test procedure, we propose a new estimator that views time as a continuous covariate to perform post stratification with a sample-dependent number of stratification levels. We prove central limit theorem in a natural limiting regime under non-stationarity, so that valid large-sample statistical inference is available. We show that the proposed estimator achieves the optimal asymptotic variance among all estimators. When the experiment design phase of an A/B test allows, we propose a new time-grouped randomization approach to make a better balance on treatment and control assignments in presence of time non-stationarity. A brief account of numerical experiments are conducted to illustrate the theoretical analysis.