Dottin (45) and Stafanie Taylor (47) helped the Windies make 114-8.
Jhulan Goswami's rapid 26 from 19 balls left India needing 10 from the last over, bowled by Dottin (3-16), but they fell short on 111-9 in Mohali.
It means England must beat Pakistan later to be sure of qualification, as a heavy defeat would risk elimination.
A Pakistan win would leave them, West Indies and England all on six points, with the two teams with the best net run-rate going through.
Renowned as one of the biggest hitters in women's cricket, Dottin did not clear the ropes on this occasion but the Barbados all-rounder's 45 from 40 balls, including five fours, provided the acceleration they required to set a competitive total.
Only captain Taylor, who added 77 with Dottin for the fourth wicket, offered support as the other seven Windies batters contributed just 18 runs between them against India's five-pronged spin attack.
India lost captain and batting kingpin Mithali Raj to the first legal delivery of the innings, but Dottin's right-arm seam was introduced for the fourth over and she took a wicket with her first ball to remove Veda Krishnamurthy, who had smashed four early boundaries.
Although India were already eliminated, Goswami and Anuja Patil (26) threatened a consolation victory in front of a growing crowd arriving early for the India-Australia men's game, Dottin held her nerve to pick up two wickets and a run-out in the last over.
West Indies must wait for England's game with Pakistan to find out their semi-final opponents. The group winners will face Australia in Delhi on Wednesday, the runners-up meet unbeaten New Zealand in Mumbai on Thursday.
Deandra Dottin starred with bat and ball as West Indies booked their place in the semi-finals of the Women's World Twenty20 with a narrow win over India.