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Tyler Hansbrough knocked the ball away from FSU's Isaiah Swann with just over eight seconds remaining. Al Thornton was able to corral the loose ball and fire off a desperation attempt, but his 30-footer fell well short as time expired.
"This does a lot for our momentum and our confidence," Hansbrough said. "It kind of gets that taste out of our mouth. It's always a much better feeling to go home with a win."
The Tar Heels benefited from a scorching perimeter effort - UNC shot at over a 75 percent clip from beyond the arc for much of the game before finishing 13-of-21 (62 percent).
Leading the way was junior Wes Miller, who made the most of his first career start by connecting on 6-of-10 3-pointers and tallying a team-high 18 points.
Miller's final connection gave UNC a 79-78 lead with 54 seconds to play and snapped his team out of a seven-minute funk in which just one field goal was managed.
"We knew these guys were all good shooters," UNC coach Roy Williams said. "If you worry too much about shooting, it'll turn you into a bad shooter. We didn't talk about it too much and it took care of itself.
"When the ball goes in the basket things look so much prettier."
Terry (17 points), Hansbrough (15), Danny Green (11) and Byron Sanders (10) also turned in double-digit scoring outputs for the balanced Heels. Miller and Sanders contributed career highs in minutes and points.
Though it wasn't his most aesthetic performance, Hansbrough contributed when it counted. After picking up three fouls in the first half, the freshman post player turned in consecutive three-point plays to begin the second half as UNC carved into FSU's 50-42 halftime lead.
Williams credited the foul-saddled Hansbrough for playing smart enough to stay in the game and creating a presence that opened up the perimeter.
"He's such a threat, you are going to have more open shots if they choose to make that their emphasis," Williams said.
Thornton and Swann led the Seminoles with 19 points apiece. Swann was the catalyst in the first half, pouring in 17 points as FSU used an 11-0 run to build a lead that swelled to 13 points at one juncture.
A pair of jumpers by Green - another player Williams said he was tempted to inject into the starting lineup - in the final minute before intermission trimmed the FSU advantage to eight.
Miller hit a 3 with 15:09 that ignited a 19-4 run that gave the Tar Heels command of the game before the Seminoles battled back late.
"I just tried to approach this game just like I would any other," Miller said. "My teammates found me, that's what it boiled down to. My teammates made plays, got me looks and I was fortunate enough to knock them down."
UNC returns to action Wednesday night when it hosts ACC newcomer Boston College at the Smith Center.