An Indian electricity system with very high shares of solar photovoltaics seems to be a plausible future given the ever-falling solar photovoltaic (PV) costs, recent Indian auction prices, and governmental support schemes. However, the variability of solar PV electricity, i.e., the seasonal, daily, and other weather-induced variations, could create an economic barrier. In this paper, we analyzed a strategy to overcome this barrier with demand-side management (DSM) by lending flexibility to the rapidly increasing electricity demand for air conditioning through either precooling or chilled water storage. With an open-source power sector model, we estimated the endogenous investments into and the hourly dispatching of these demand-side options for a broad range of potential PV shares in the Indian power system in 2040. We found that both options reduce the challenges of variability by shifting electricity demand from the evening peak to midday, thereby reducing the temporal mismatch of demand and solar PV supply profiles. This increases the economic value of solar PV, especially at shares above 40%, the level at which the economic value roughly doubles through demand flexibility. Consequently, DSM increases the competitive and cost-optimal solar PV generation share from 33–45% (without DSM) to ~45–60% (with DSM). These insights are transferable to most countries with high solar irradiation in warm climate zones, which amounts to a major share of future electricity demand. This suggests that technologies, which give flexibility to air conditioning demand, can be an important contribution toward enabling a solar-centered global electricity supply.