Cave deposits from India and China have been widely used to infer past strength of the Indian and East Asian summer monsoons, as the isotopic composition of oxygen (d18O) in stalagmites is primarily controlled by the d18O of precipitation. These stalagmites show spatially and temporally coherent variability in oxygen isotopes throughout the ice age. Here we use a climate model with an embedded module for oxygen isotopes to show that a sudden increase in North Atlantic sea ice extent during the last glacial period cools the Northern Hemisphere, reduces precipitation over the Indian basin and weakens the Indian monsoon. In turn, the precipitation weighted d18O is increased over India and isotopically heavier vapor is exported to China. The model broadly reproduces the proxy evidence of abrupt climate changes associated with an archetypal Heinrich event and the abrupt changes in d18O seen in stalagmites across China, which are tape recorders for the strength of the Indian monsoon and not the East Asian monsoon, as previously thought. The implication of our results for Dansgaard-Oeschger events and precessional cycle variations seen in these cave records will be discussed.