Burke, a rising senior, won the event, shooting an 11-under-par 66-65--131 while Castleberry, a rising sophmore, followed in third with a 67-69--136.
Playing at par-71 Pine Hollow Golf Club, Burke, the Conference Carolinas Player of the Year and Barton's Male Athlete of the Year, used a hole-in-one Sunday to edge former N.C. Amateur Champion Dale Fuller by two shots.
Burke, a product of Charles B. Aycock High School, carded three eagles, three birdies, two bogeys and one double in his opening-round 66, which left him two shots behind Fuller, who played collegiately at Clemson.
On Sunday, Burke fired a 65 that included a hole-in-one with a 8-iron on the 175-yard fifth hole, six birdies and two bogeys. The hole-in-one was his first, witnessed by a number of residents who were outside their homes watching the golf.
"I just hit it, looked up and could tell it was going to be close," Burke said in a press release. "When it went in, I said 'All right!' and held my hands up in the air.
"All the fans were screaming and jumping up and down like it was a big tournament. Daniel was playing ahead of me, and when it went in, he was jumping up and down."
Playing in Sunday's final twosome, Burke's ace pulled him within one shot, followed by a birdie on the sixth hole to pull even, finishing the front side with a 30 and a one-shot lead.
Fuller, who has twice advanced to the final stage of PGA Tour Qualifying School, finished Sunday shooting 69.
Last year, Burke lost to UNC-Pembroke signee Jordan Walor in a playoff when Walor birdied the first two holes.
Burke adds the Wake championship to an already solid summer after taking third in the Wayne County Amateur.
He noted that while he was a favorite in Wayne County, "nobody knew me up here (Wake County), so there was no pressure to win."
With Castleberry as his caddie, Burke qualified on Thursday this past week for the Carolinas Amateur by firing a 73, tying him for 13th, at Bentwinds in Fuquay-Varina.