Chasing 171, Australia recovered from early setbacks through a match-winning 100-run fourth-wicket partnership between Ellyse Perry and Ashleigh Gardner. Perry made 56 from 38 balls and Gardner finished unbeaten on 53 off 29 as Australia reached the target with an over to spare.
The defeat ended India's hopes of adding the T20 title to last year's ODI World Cup triumph and marked a second successive group-stage exit. South Africa, who had earlier beaten Bangladesh, joined Australia in the semi-finals and will face England.
India had posted 170-4 after captain Harmanpreet Kaur produced a brilliant late assault, smashing 56 from just 27 balls with six fours and three sixes. Openers Smriti Mandhana and Shafali Verma had earlier put on 66 for the first wicket, while Jemimah Rodrigues made 34 before being retired out.
Australia's chase started badly when Georgia Voll fell to the second ball, but Phoebe Litchfield and Beth Mooney steadied the innings before India struck again to leave the favourites at 68-3 in the 10th over.
With 99 runs needed from the final 10 overs, Perry and Gardner gradually wrestled back control. Gardner's power hitting and Perry's calm accumulation shifted the momentum before both reached half-centuries in the closing stages.
Perry eventually departed for 56 with victory in sight, and Georgia Wareham hit the winning runs to complete a memorable chase and maintain Australia's perfect record in the tournament.
Australia will face West Indies in Tuesday's semi-final, while England take on South Africa at The Oval on Thursday.
The South African Women were made to work hard for runs as they eventually chased down 117 to defeat Bangladesh by four wickets in the Women's T20 World Cup at Lord's on Sunday.
England Women kept their winning streak alive when they defeated New Zealand by nine wickets in their T20 World Cup clash at The Oval on Saturday night.
England booked their place in the T20 World Cup semi-finals with a match to spare after securing a convincing 38-run victory over West Indies at Lord's.
Australia Women star Ellyse Perry wrote another chapter in her storied career by almost single-handedly guiding her side to an 113-run win over Pakistan at the ICC Women's T20 World Cup.
