Skipper Stafanie Taylor (40) anchored the Windies' innings of 103-8 in Chennai, but lacked support as left-arm spinner Anam Amin took 4-16.
Captain Sana Mir nearly saw Pakistan home but fell in the final over.
There was also concern for Pakistan opener Javeria Khan, who was hit on the head by a Shamilia Connell bouncer and was taken off on a stretcher.
Wisden India journalist Himanish Bhattacharjee later tweeted that Javeria had been taken to hospital for a precautionary CT scan, but was "OK".
England face Bangladesh in their first game on Thursday, also in Group B.
West Indies avoided an upset as they beat Pakistan by four runs in their Women's World Twenty20 opener.