Field observations and geodetic measurements suggest that in the central part of the Karakoram Mountains, glaciers are either stable or expanding since 1990, in sharp contrast to glacier retreats that are prevalent in the Himalayas and adjoining high-altitude terrains of central Asia. Decreased discharge in the rivers originating from Karakoram is cited as a supporting evidence of this somewhat anomalous phenomenon. Here, in contrary to those citations, we show that, river discharge during the melting season of the glaciers in central Karakoram has increased from 1985 to 2010. We have implemented a sophisticated statistical procedure involving non-parametric tests combined with a benchmark smoothing technique that has proven to be a powerful method for empirical trend analysis to remove the stochastic component from the trend component in a time series. Melt water from winter snows is the dominant constituent of June and July flows. Glacial melts predominantly contribute to August and partially to September flows, which are controlled by monsoonal snowfall too at elevations approximately >3500 m. For all four summer months, flows increased from 1985 to 2000. August flows, which actually reflect the states of the glaciers, have continued to rise steadily after 2000 at the same rate as those did for the period 1985-2000. However, the rising trends of June and July flows changed to slightly declining trends from 2000 to 2010. These trends most likely indicate drop in winter snowfall over Karakoram and do not provide direct indications about the states of the glaciers. The rising trend of August discharge is due to change in glacial storage at a steadily decreasing rate of approximately 0.04-0.05 mm/day/year for the period 1985-2010. This rate is nearly equal to the rate of increase in precipitation during the summer months over Karakoram Mountains in recent decades as determined from the ERA-40 and GPCP precipitation datasets. Thereby, this is most plausibly, why the glacial mass balance in central Karakoram is nearly neutral. The rising river flows accompanying non-negative glacier mass balance are consistent with predicted future river flows derived from hydrologic modeling coupled with a climate projection suggesting increasing temperature and precipitation with unchanged glacier covers. This investigation reconciles two apparently contradictory observations namely rising river flows and either zero or slightly positive mass balance of central Karakoram glaciers.