I don't think the Wildcats will necessarily stop UNC's perimeter shooting, but that doesn't mean they don't present a danger. Villanova has an impressive list of scalps for the season, including twice beating Pittsburgh, Marquette, and Syracuse and wins over Duke, UCLA and Notre Dame. Of course, they've lost to as many good teams as they've beaten (They're 9-7 against teams in the Top 40 of Ken Pomeroy's ratings), but if they want the upset, here's how the Wildcats will go about it.
First, despite what you may think, they won't slow the game down. In their two wins over Syracuse, they ran right at the Orangemen's pace, outscoring them 102 to 85 and 89 to 86. They'll try to work the ball into Dante Cunningham a lot, and penetrate with their guards to pick up fouls and disrupt UNC's interior defense. Villanova won't attempt a Duke-level number of threes - it's the main difference between the two similarly built teams - but they'll need someone to get hot, typically Scottie Reynolds or Corey Stokes, the two players who take more threes than twos. They'll go for the steal a lot, again like Duke, but they're also prone to fouling. This won't have an effect on their depth, unless Cunningham hits the bench early and gives the UNC front line a chance to feast upon his smaller teammates, but they should probably avoid sending UNC to the line if they can hep it.
Offensive rebounding will be important for the Wildcats, and there are only two starters who contribute in that regard, Cunningham and Dwayne Anderson, the 6'6" wing player built in a Danny Green mold. Keeping UNC off the offensive boards on the other end will be critical, though, and the Wildcats typically do well as a team in that end. Of course that's in part because they bait their opponents into taking so many threes; if they can do that against Carolina by denying entry passes and otherwise frustrating them like Maryland and Wake Forest did, that should go a long way to getting Villanova the win.
Overall, I don't think they can do it. This Tar Heel team is too talented and too determined to slip up at this stage. Of course, I thought the same thing a year ago, and that turned out... poorly. Hopefully the Carolina team remembers this as well, and doesn't make the same mistake twice.