In doing so, they became the first rookie champions of the event in 11 years.
Theegala was able to overcome a pulled muscle early in his round to sink a 20-foot birdie putt on the last hole for that secured victory in the 54-hole exhibition event at Tiburon in Naples, Florida.
The eventual winners were tied for the lead with countrymen Ryan Palmer and Charley Hoffman on the final green.
Hoffman ultimately missed from 12 feet to give Hoge and Theegala the triumph.
"It's nice to get a little taste of competition and taste of victory because it's so hard out here, so many great players," Theegala said. "Feels really, really good."
Matt Kuchar and Harris English finished third.
Theegala, the son of Indian immigrants, revealed the injury that set him back on the first hole of the final round.
"I made a bad swing on the first hole and I kind of saved it and I pulled my oblique," he said.
"It got better as the round progressed. I knew it wasn't too big of a deal so I was just trying to keep my partner in it. Tom played so well. It started freeing up at the end so I was able to make a couple better swings."
Hoge said they needed to hang in there over the opening seven holes.
"With Sahith on the first hole getting a little banged up, I knew I was going to have to carry him a little bit off the start," Hoge said.
"I knew he was going to hit some good shots for me down the stretch like he did and what a great putt at the last."