The Tibetan Plateau is among the region’s most sensitive areas to global climate change. The observation data from 113 meteorological stations on the Tibetan Plateau and surrounding regions in China for 1971–2017 were used to analyze the periodic oscillations and trends in precipitation and extreme precipitation on multiple time scales to ensemble empirical mode decomposition. The relationship between extreme precipitation and sea-surface temperature (SST) anomalies was also explored. The results were as follows. (1) The timing of extreme-precipitation events in the highlands is consistent, with increased total precipitation and increased frequency, intensity, and extreme values of extreme precipitation. (2) Changes in temperature and precipitation are not completely synchronized. The total extreme precipitation, number of extreme-precipitation days, maximum single-day precipitation, and extreme single-day precipitation intensity all showed increases with fluctuations; the quasi-3-year oscillation contributes the most to the extreme precipitation. PRCPTOT is most strongly correlated with R10 and R95p. (3) The spatiotemporal patterns of the first and second empirical orthogonal function modes of the indices differed significantly and were not spatiotemporally uniform, but exhibited local clustering. (4) The Indian Ocean Warm Pool Strength and Western Pacific Warm Pool Strength indices were most highly correlated with each extreme-precipitation index, and the timings of the extreme-precipitation events lagged behind those of the SST anomalies. This study improves our understanding of extreme precipitation events in the context of climate warming and provides a basic analysis for the further assessment and prediction of extreme precipitation on the Tibetan Plateau and the surrounding ecologically fragile areas.