After jumping ahead 22-12 by halftime, the Wildcats gave up 17 points in the third quarter to allow Kanab to close the gap to just one point heading into the last period of play.
That's when the South Summit team leaders stepped up, ensuring the Wildcats wouldn't be exiting the playoffs early.
Junior forward Beau Rydalch knocked down his free throws in the fourth quarter, and junior guard Brad Richins started heating up from the outside, hitting a couple big three-pointers.
South Summit coach Dusty Hatch said the Wildcats can play much better than they did on Saturday, but that he's happy they battled their way to a win.
"We weren't very good," he said. "We really struggled. But it's just survive and advance. It's a lot of pressure and we felt fortunate to get out of that game with a win."
He added that he hopes the team can get back to playing with the intensity it had at the end of the regular season.
"Hopefully we've got our bad game behind us and we can move on and play the way we're capable of playing," he said.
Rydalch led the way with 20 points for the Wildcats, adding a strong performance on the boards.
"He got a lot of rebounds in crunch time," Hatch said. "He was one of the bright spots on the team he just went out and played."
Brad Richins scored 10 points, the only other South Summit player to reach double digits.
"Brad hit two big threes with just a couple minutes left that put us up by three," Hatch said, adding that the Wildcats were able to close out the victory after that.
South Summit (15-7) will travel to Cedar City on Thursday for an 11 a.m. state quarterfinal game against Gunnison (15-7). The Wildcats defeated Gunnison on Dec. 14.
"They're a really good team," Hatch said. "But we do match up well with them."