Rahul scored his second T20I century during the first match of the series last week scoring 101 not out to guide India to an eight-wicket victory over England in Manchester.
Rohit Sharma, who blasted his third hundred in T20Is, also reaped reward for his brilliant batting display as he jumped two places to No.11.
However, India skipper Virat Kohli slipped four places to No.12 after scores of 0, 9, 20*, 47 and 43 in five matches against Ireland and England.
Finch, the new captain of the Australian T20I side, had a remarkable run during the tournament in Zimbabwe, scoring 68*, 172 – a world record in the format, 16, 3 and 47.
Finch rose three spots from No.4 to become the new No.1 batsman. He played no small role in Australia bouncing back from a spate of losses across formats in recent times, but it was still not enough for his team to win the tri-series title.