Horschel went into the final round with a five-shot lead, but saw his advantage tumble after playing partner Wise two-putted on the 15th for his fourth birdie of the day.
Despite this, Horschel was able to produce a timely response as he holed from 53 feet for his first eagle at the event in 573 holes.
The 35-year-old then cruised to victory as he beat Wise by four shots and finished six ahead of defending champion Patrick Cantlay and Joaquin Niemann.
"It feels pretty good," Horschel told Sky Sports. "I felt comfortable all day, never felt like my heart was beating too fast, never was worried about anything and just trying to play within myself and play my own game.
"I felt like that was all I needed to do, knowing the conditions were tough and if someone went out and played a really special round of golf and nicked me, then hats off.
"But I played really solid today and really happy with it. I've never won a tournament with my wife and kids at it and for them to finally be here at a tournament I've won is so special."
World number two Jon Rahm carded a closing 69 to finish in a tie for 10th. Last year, the player enjoyed a six-shot lead after 54 holes before having to withdraw due to a positive Covid-19 test.
Rory McIlroy, on the other hand, produced rounds of 73 and 74 over the weekend as he slipped into a tie for 18th.
The four-time major winner covered the first nine holes in 41 during the final round, before responding with birdies on the 12th, 14th and 15th.