Chasing 135 to win, Gujarat lost both openers -- Ishan Kishan (16) and Brendon McCullum (3) -- to be reduced to 23-2 but Finch blasted 5 fours and 6 sixes in his scintillating 34 -ball 72-run innings as the visitors romped home with 6.1 overs to spare.
Earlier Tye returned with a three-wicket haul to trigger a top-order collapse as Royal Challengers Bangalore were bowled out for 134 by Gujarat Lions after electing to bowl in their eighth match of IPL 10.
Besides Tye, Ravindra Jadeja (2/28) snapped two wickets and Basil Thampi (1/34) and Ankit Soni (1/28) picked up one wicket each as Lions dished out a disciplined bowling performance.
For RCB, Pawan Negi (32) and Kedar Jadhav (31) were the top scorers.
This is only the third victory in the season for Gujarat Lions, who had gathered just four points from seven games to be languishing at the bottom of the table.