The impact of climate extremes, such as heat waves and extreme rainfall, can cause harvest failures, flooding, and droughts that ultimately threaten global food security, harming the region’s economy. Fluctuations in streamflow indicate the sensitivity of streamflow responding to extreme precipitation events and other climatic variables (temperature extremes) that play a significant role in its generation. Pakistan is also considered one of the climate change hotspot regions in the world. The devastating impacts have often occurred in recent decades due to an excess or shortage of streamflow, majorly generated from the Upper Indus Basin (UIB). To better understand climate extremes’ impact on streamflow, this study examined climate extremes and streamflow (Q) changes for three decades: 1990–1999, 2000–2009, and 2010–2019. Observed streamflow and meteorological data from nine sub-catchments across all climatic zones of the UIB were analyzed using RGui (R language coding program) and partial least squares regression (PLSR). Climatic variables were estimated, including precipitation extremes, temperature extremes, and potential evapotranspiration. The Mann–Kendal test was applied to the climatic indices, revealing that precipitation increased during the last 30 years, while maximum and minimum temperatures during the summer months decreased in the Karakoram region from 1990 to 2019. The spatiotemporal trend of consecutive dry days (CDD) indicated a more increasing tendency from 1990 to 2019, compared to the consecutive wet days (CWD), which showed a decreasing trend. PLSR was applied to assess the relation between climatic variables (extreme P, T indices, and evapotranspiration). It was found that the dominant climatic variables controlling annual streamflow include the r95p (very wet days) and R25mm (heavy precipitation days), maximum precipitation event amount, CWD, PRCPTOT (annual total precipitation), and RX5 (maximum five-day precipitation). The TXn (Min Tmax) and Tmax mean (average maximum temperature) dominate streamflow variables. Moreover, the impact of evapotranspiration (ET) on variations in streamflow is more pronounced in arid catchments. Precipitation is the predominant factor influencing streamflow generation in the UIB, followed by temperature. From streamflow quantification, it was found that climate-driven annual streamflow decreased during 1999–2019 in comparison to 1990–1999, with an increase in a few catchments like Kalam, which increased by about 3.94% from 2000 to 2010 and 10.30% from 2010 to 2019, and Shigar, which increased by 0.48% from 2000 to 2009 and 37.37% from 2010 to 2019 concerning 1990–1999. These variations were due to changes in these climatic parameters. The PLSR approach enables the identification of linkages between climatic variables and streamflow variability and the prediction of climate-driven floods. This study contributes to an enhanced identification and hydroclimatological trends and projections.