Seven players began the final round tied for the lead, but it was Finch who made the biggest charge, shooting a 6-under 66 to get into contention. Dodt answered with birdies at Nos. 16 and 18 to get to 14 under, good enough for his first European Tour victory.
Richard Bland shot 71 to finish in a group at 12 under, along with fellow Brits Barry Lane and David Drysdale and Tetsuji Hiratsuka. The Japanese player shot 71 two days after his round of 62 set the course record.
Dodt, whose previous best finish was a tie for ninth at last year's Barclays Singapore Open, began the day one shot off the pace but picked up three strokes by the turn and was well placed with nine holes to play.
A bogey at the 11th threatened to derail the 24-year-old's bid, but he managed to recover over the final three holes to secure the trophy.
Finch, meanwhile, mounted his charge from down the leaderboard. He shot 32 on the front nine with five birdies and a bogey,but only picked up two more shots down the stretch.
Bland's 66 had catapulted him into contention on Saturday, and two early birdies allowed him to keep pace at the top of the scoreboard. A bogey at the sixth set him back, and although he recovered a shot at the 16th, he wound up with a bogey at 18 to stay winless on the tour.