Australia began to take control again when Kaur fell run out after getting her bat stuck in the ground as she tried to slide it into the crease.
“Can’t be unluckier than that,” Kaur said of her run out. “Putting the effort in was important and we were happy to go to the last ball. We wanted to fight till the last ball.”
Australia has won five of the seven T20 World Cups played, only missing out in 2016 when it lost to West Indies in the final and in the first tournament in 2009 when it lost in the semis.
It has now made every final after 2009 and will play either England or host South Africa, who meet in the second semifinal on Friday.
Australia’s score against India was down to its top four batters, with Healy getting 25, fellow opener Beth Mooney 54 off 37, Lanning 49 not out and Ashleigh Gardner 31 from 18.
India also paid for a couple of crucial misses. Wicketkeeper Richa Ghosh dropped a catch off Lanning when the Aussie captain was on 1. Mooney was dropped on 32.