Tobey also came down with a critical rebound and hit two free throws with 7 seconds left to make it a two-possession game, then Brogdon hit two more with 1.4 seconds left to seal this grind-it-out win.
Virginia shot 37 percent, but relied on its defense. N.C. State (14-11, 5-7) shot just 33 percent for the game and 3 for 17 from 3-point range.
Trevor Lacey scored 14 points to lead the Wolfpack, though he missed a driving shot for the tie in the final seconds to set up Tobey's free throws.
Anthony "Cat" Barber added 11 points for N.C. State, but outside shooter Ralston Turner managed just four points and went 0 for 6 from 3-point range while playing with a balky knee — a critical lack of production on a night when neither team led by more than six points.
Worse, this was a huge opportunity for N.C. State to bolster its NCAA tournament chances. But instead of earning a marquee win, the Wolfpack fell for the sixth time in eight games since upsetting then-unbeaten Duke on Jan. 11.
As for Virginia, the Cavaliers missed Anderson, their No. 2 scorer at 13.4 points and the league's top 3-point shooter at 48 percent.
Anderson broke a finger on his shooting hand late in the first half of last weekend's win against Louisville, an injury that required surgery and left him sitting on the bench with his hand heavily bandaged as junior Evan Nolte started in his spot.
Virginia's offense didn't look very efficient as it adjusted to Anderson's absence, but Tobey's second-half spark helped jolt the Cavaliers.
The Cavaliers got a boost when Wolfpack freshman Caleb Martin was called for a flagrant foul for running into Nolte going back up the court after a Wolfpack basket. Brogdon hit 1 of 2 free throws, then Tobey followed with a three-point play that pushed the lead back up to 42-37 with 4:44 left.
Then, when N.C. State got back within a point on Lacey's scooping layup, Tobey threw down a dunk off a pick-and-roll pass from Brogdon to make it 45-42 with 1:18 left.