Deepti Sharma gave Velocity a last-minute scare but the partnership between Danielle Wyatt and Mithali Sharma was enough to take them over the line.
England lost their final seven wickets for 25 runs to be bowled out for 136.
Indian women's team will play a three-match ODI series at home against England, starting February 22.
The White Ferns chased down the target in 29.2 overs to register a morale-boosting win.
While India skipper Mithali Raj was selected to lead the World Cup team, Harmanpreet Kaur and Deepti Sharma were also included.
The India women's team will play hosts England in the final of the ICC Women's World Cup at Lord's on Sunday.