In the last second leg league match, amid mounting tension, the seventh wicket pair of C L Fitzpatrick and J M Purves added an unbeaten 47 runs in 7.1 overs to help the Aussies secure a four wicket win and a place in the final.
Earlier, Australia restricted India to 230 for nine and replied with 231 for six in 50 overs.
Fitzpatrick, who scored a 29-ball 31 with three fours, scampered through for a single off the last ball after cutting Goswami to point to trigger jubilant scenes in the Aussie camp.
In another last league match, New Zealand defeated England by 27 runs to top the league with 21 points (five wins from six matches).
Australia finished with 18 points followed by India (13) and England (zero).
The Aussies got off to a blazing start with Bulow (85, 91 balls, 12x4) and L K Poulton (27, 75 balls, 2x4, 1x6) adding 74 for the first wicket in 21.3 overs. Bulow added a further 59 in 11 overs for the second wicket with Rolton (29, 41 balls, 2x4) to put the innings on a firm footing.
However, India struck back and reduced the rivals from 133 for one in 32.2 overs to 152 four in 35.1 overs. India sensed victory picking up to more wickets to reduce the Aussies to 184 for six in 42.5 overs, before judicious batting by the seventh wicket pair put paid to the hopes of Indians.
Earlier, electing to bat first, India rode on half centuries by opener Karuna Jain (75, 119 balls, 13x4) and middle-order bat Hemlata Kala (54, 41 balls, 6x4, 1x6) to post a modest total of 230 for nine after a top order collapse.
Placed in a must-win situation, India lost Jaya Sharma (14) and skipper Mithali Raj (nine) early.
Karuna and Anjum Chopra, returning to the side after being dropped for the previous two matches, arrested the slide with a 68-run stand in 16.5 overs before the home side lost their way.
From 117 for two, India lost Karuna, R Dhar (0), Anjum, A Sharma (5), Goswami (2).
However, Kala exploited the slog overs with a 41-ball 54 to give the total a modicum of respectability.
The Australian bowlers did well to restrict the Indians in the early half of the innings but the batsmen cut loose once the spinners came on and added 126 in the last 20 overs at more than six an over.
India 230 for 9 in 50 overs (Karuna Jain 75, Hemlata Kala 54, Anjum Chopra 41; Lisa Sthalekar 3 for 64, Sampson 2 for 33, S J Andrews 1 for 26) lost to Australia 231 for 6 in 50 overs (M J Bulow 85, Fitzpatrick 31 n o, Karren Rolton 29, Poulton 27; Nausheen al Khadeer 2 for 48, Rumeli Dhar 1 for 24) by 4 wickets. Australia by virtue of this win make it to final.