The India national cricket team toured Zimbabwe from May to July 2001 and played two Test matches against Zimbabwe, with each team winning one Test match. This would be Zimbabwe's only Test victory over a side other than Bangladesh until they beat Pakistan in the second Test in 2013.
India and Zimbabwe also participated in a triangular Limited Overs International competition with West Indies which was eventually won by West Indies.
Test series summary
References
Indian cricket team in Zimbabwe in 2001 Wikipedia(Text) CC BY-SA