Robinson scored 26 points and fellow North Carolinian Ky Bowman had 24 for the 12th-seeded Eagles (19-14), who will face No. 4 seed Clemson on Thursday in the quarterfinals at Barclays Center.
The fifth-seeded Wolfpack (21-11) wiped out a double-digit deficit in the final 10 minutes and tied it five times down the stretch, the last on two free throws by Torin Dorn with 40.7 seconds left to make it 85-all.
Then BC let Robinson, runner-up for ACC player of the year, take over.
Robinson dribbled away from the screen, left N.C. State big-man Omer Yurtseven behind and let go with a smooth jumper from about 10 feet to give BC a lead.
On the ensuing possession, Robinson was on the in-bounder as N.C. State tried to get it in from the front court, and got a hand on the ball. Bowman came up with it and was fouled. He made two shots to put BC up four.
"In my first two years we had two ACC wins, and we knew that was just a process," said Robinson, a junior from Raleigh. "And, I mean, I stuck with it, with Coach. We just listened to Coach, and he had the vision."
Markell Johnson cut it to two with 7.3 left, but then he called a timeout when the Wolfpack didn't have one and was called for a technical. Robinson made two more free throws to seal the victory.
"I knew in my head we didn't have any," Johnson said. "I was so caught up in the game."
Yurtseven had 18 of his 20 points in the second half and Allerik Freeman had 21 for North Carolina State.
Boston College: The Eagles had not won more than one game in any ACC Tournament since 2006, BC's first season in the conference. The Eagles also became the first team since the ACC expanded to five days in 2014 to win an opening day game and follow it up with a victory on day two.
N.C. State: The Wolfpack led only once, 2-0. They never did figure a way to stop Bowman and Robinson, but maybe the biggest problem was on the boards. N.C. State was outrebounded 39-31 and gave up 13 offensive boards and 15 second-chance points.
Boston College center Nic Popovic hit the floor during a small pileup while going for a loose ball with about 12:30 left in the first half. At first, he got up and started making his way back on defense, but after about three steps he stopped and went to the floor just short of midcourt, grabbing his lower right leg. He hopped to the bench and eventually was helped to the locker room. Popovic returned and re-entered the game with about seven minutes left. The sophomore, who had a career-high 20 points in the opening round against Georgia Tech, finished with 15 points and seven rebounds.
Boston College: The Eagles lost 74-70 to Clemson at home on Jan. 3.
N.C. State: The Wolfpack are in fine shape for an at-large NCAA bid despite the early exit here.
WATCH: Gov. Roy Cooper says Pack 'easily' in the NCAA Tournament
Louisville 82, Florida State 74
In Wednesday's first game, Louisville advanced by beating Florida State.
Quentin Snider scored 19 points, Ray Spalding had 18 and the Cardinals knocked off the Seminoles 82-74 in a tournament game with major NCAA implications.
"I'm sure this significantly helps our resume," said David Padgett, the interim coach who took over when Rick Pitino was fired before the season. "I know if we're able to come out and get a win (Thursday) against the No. 1 team in the country that I would surely think they're in."
Deng Adel added 15 points and eight rebounds for the ninth-seeded Cardinals (20-12), who won for the first time in ACC postseason play and advanced to face top-ranked Virginia in the first quarterfinal Thursday.
The Associated Press contributed to this report.