The Queenstown player became one of just three players to claim three wins on the Charles Tour with victory in the Mount Open.
He shot 19-under-par to claim a two-stroke win from from Daniel Hillier.
After shooting rounds of 68 and 64 on the first two days, he edged ahead on Saturday.
In blustery conditions he shot a round of 69, taking him to 15-under and one shot ahead of Hillier.
He extended that lead by another shot yesterday, firing a 4-under 68 to hold on to the leading spot.
Three early birdies were offset by two bogeys on the seventh and eighth.
However, he responded with three more birdies, before a key birdie on the 15th was followed by a bogey from Hillier on the 16th.
Anstiss was thrilled to get the job done.
“This is an awesome feeling," he said.
"It’s never easy to win a golf tournament and I had a real battle on my hands with Dan [Hillier] and Kit [Bittle].
“Dan put it on me early. I think he had the lead through the first six or seven holes and I just kept pressing.
"I made a couple of really good saves along with some key birdies late in the back nine and managed to get over the line."