Objective of this study is to empirically investigate the time varying co-movements between crude oil and Indian stock market returns both at aggregate and sector level. This study uses weekly closing prices for Brent Crude, BSE-Sensex and seven sector indices of Bombay Stock Exchange namely Automotive, Energy, Financial, Industrial, Metal, Oil & Gas and Power as data input. The data span of this study runs from January 1, 2006 to Feb 28, 2015, which encompasses the booming, recessionary and the recovering phase of global as well as Indian economy. The paper deploys VAR-DCC-GARCH framework. Three versions of GARCH namely standard, threshold and exponential and both symmetric and asymmetric versions of dynamic contemporaneous correlations have been used. Results of the study indicate that direct volatility spill over from oil market to Indian stock market is not significant at the aggregate level; however, it is significant in case of auto, power and finance sector. Parameter of dynamic correlations and volatility were significant thereby providing empirical evidence of the time varying differential dependence of Indian stock sector indices on oil price fluctuations. Outcomes of this study highlights that investors attempting to diversify, their investments should always consider dynamic volatility and correlation linkages so as to maximize returns and minimize risk.