Last week, Thorpe won the rain-shortened Kroger Classic and with the win on Sunday, he joined Larry Nelson as the only players to win two in a row this year on the elder circuit.
Nelson and Thorpe were the only players to win consecutive tournaments last year as well, and all four of Thorpe's wins on the Senior Tour have come after September.
'I win everything after September,' said Thorpe, who won $262,5000 for the victory. 'It takes me eight months to warm up.'
Bruce Lietzke finished alone in third place at 11-under 202.
Thorpe's lead was down to two after Lietzke ran home a 15-foot eagle putt at the 15th hole. Thorpe ran the margin up to three at the same hole after he drove into a left fairway bunker. He had no choice but to lay up short of a creek, where he wedged his approach to tap-in range to set up birdie.
Thorpe extended his lead at the next hole, the par-3 16th, when his 7-iron from the tee landed 13 feet from the hole, giving him his second birdie in a row.
With a four-shot lead, Thorpe missed two par saves at the last two holes and coupled with a four-foot birdie by Morgan on No. 18, gave him a two-shot win.
'I play courses like this well,' said Thorpe. 'You have to manage your game on courses like this. I made 19 birdies this week but I'm proud that I birdied some of the harder holes.'
The fact that this tournament finished on time is impressive. On Thursday, an apparent tornado ripped through the course at the Glen Oaks Country Club, causing considerable damage. The thunderstorms were so severe that spectators and volunteers were forced to evacuate the course. Sunday was not beautiful with some rain, but there were no delays.
Thorpe three-putted for bogey at two but he ran off four front-nine birdies, including a 20-footer at seven and a two-putt from 30 feet at the ninth.
Tom Kite and Isao Aoki, both of whom were one shot behind Thorpe coming into the final round, carded 2-under 69s on Sunday to finish tied with Bruce Summerhays for fourth at 10-under par.
Full-field scores from the Allianz Championship