After being put into bat, India were 69 for two after 16 overs when play was stopped due to rain at 5pm local time (11:30 IST) and after a wait of three hours the umpires decided to call off the match.
The two teams take two points each from today's match, which means that the final league game between India and England on January 30 at the WACA in Perth will be a straight knockout for a chance to play Australia in the final on February 1 at the same venue.
India had lost to Australia and England in their first-leg matches of the double round robin format tournament.
The start of the match was delayed by 40 minutes due to drizzle since morning and there was first rain interruption at 3:30 pm local time (10 am IST) when India were six for no loss in 2.4 overs.
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Play resumed with India losing the struggling Shikhar Dhawan for eight in the seventh over and then Ambati Rayudu for 23 in the 13th over.
Rayudu was dismissed off the bowling of Marsh with David Warner taking a sensational catch. The Indian batsman had charged and slashed at the ball, carving it high over the infield on the off side and Warner ran from the cover to take a well-judged catch.
Rayudu faced 24 balls from which he hit two boundaries and one six.
Ajinkya Rahane was batting on 28 while Virat Kohli was giving him company on three when rain stopped play. Rahane had faced 50 deliveries from which he hit two fours.