India scored 116-6 off their 20 overs, with opener Poonam Raut topscoring with 51.
Laura Marsh ended with figures of 2-22.
England captain Charlotte Edwards made 50 not out while fellow opener Marsh contributed 39 before being stumped with England on 78.
Wicketkeeper Sarah Taylor came in to help finish the job with Edwards, the pair knocking off the target with just under three overs to spare.
Australia are also in the semis after a Duckworth/Lewis win over Pakistan, also in Galle.
Australia set Pakistan a target of 147 with Alyssa Healy and Meg Lanning producing an impressive opening stand of 53 from nine overs.
When on 38-3 after nine overs a 15-minute stoppage for rain caused the outfield to be declared unplayable.
The D/L par score was 63 and Pakistan therefore lost the match.
England and Australia have four points while India and Pakistan will only have pride to play for in their final Group A games.
In Group B, all four teams are on two points with West Indies topping it from New Zealand, South Africa and hosts Sri Lanka on net run rate.
The winners of the final fixtures will progress to the semi-finals.
The women's tournament is taking place concurrently with the men's World T20 in Sri Lanka.
Women's World T20 fixtures:
Group B: South Africa v West Indies (Galle) - Sep 30
Group B: Sri Lanka v New Zealand (Galle) - Sep 30
Group A: India v Pakistan (Galle) - Oct 1
Group A: Australia v England (Galle) - Oct 1
1st Semi-Final: Colombo - Oct 4
2nd Semi-Final: Colombo - Oct 5
Final: Colombo - Oct 7
South Africa beat Sri Lanka by 6 wickets
West Indies beat New Zealand by 7 wickets
England beat Pakistan by 43 runs
Sri Lanka beat West Indies by 5 runs (D/L)
New Zealand beat South Africa by 22 runs
Australia beat Pakistan by 25 runs (D/L)
England beat India by nine wickets