James Michael McAdoo led North Carolina (14-6, 4-3 Atlantic Coast Conference) with 17 points and 10 boards. Strickland added 14 points.
Olivier Hanlan scored 22 points, Ryan Anderson 16 and Patrick Heckmann 12 for the Eagles (9-11, 1-6).
Boston College lost its fifth straight game.
North Carolina, which entered its sixth straight week out of The AP Top 25 after spending 33 consecutive weeks ranked, opened a double-digit lead midway into the first half and coasted to the win despite losing Hairston.
The scary moment came with 4:02 left in the half when Hairston collided with Strickland as they were contesting a shot by Heckmann. After banging into his teammate while they were both in the air, Hairston fell backward to the floor and hit his head.
Hairston connected on all four 3-point attempts and hit two free throws before he was injured.
Hairston was on the floor for a lengthy time being attended by the medical staff - with coach Roy Williams at his side. After he was helped to his feet, he attempted to slowly walk to the locker room - with each arm draped over a teammate - but he appeared to become woozy and was helped to the floor where he sat until paramedics brought a stretcher.
Surrounded by medical personnel, he was carted down a long hallway past the North Carolina locker room and into a medical room in the building, where he was expected to stay for the rest of the game. He left to an ovation, with a few players from BC standing at midcourt and applauding.
North Carolina, which led by 15 at halftime, kept BC from making a charge by getting timely transition baskets early in the second half.
When BC looked like it might put a scare into North Carolina, Marcus Paige and Reggie Bullock hit 3s that helped maintain a comfortable lead.
Heckmann's three-point play had cut it to 67-56, but Bullock followed with a trey from the left wing with 7 minutes left.
The Tar Heels, ranked as high as No. 9 in the nation in November, opened the game with sloppy play. Their shooting didn't help either as they missed six of their first seven shots until Hairston entered the game and sparked a 16-2 run over a 3-minute stretch by hitting three from beyond the arc.
BC jumped to a 10-5 edge before Hairston's 3 from the right wing ignited the run. After a 3-pointer by Bullock and a short jumper in the lane by Desmond Hubert, Hairston nailed a 3 from the top of the key. Brice Johnson then sank a baseline jumper before Hairston hit another trey, making it 21-12 with 1:30 left in the opening half.
During the spree, Carolina went 6 for 6 from the floor.
The Tar Heels maintained their double-digit lead for the remainder of the half - thanks in part to three straight baskets by Jackson Simmons - and led 48-33 at intermission.
Behind Hairston's success from long range, the Tar Heels were 5 of 8 from behind the arc in the first half. They also shot 52.9 percent overall (18 of 34) and outrebounded the smaller Eagles 18-10.
The Tar Heels play their next two games at home, hosting Virginia Tech Saturday and Wake Forest on Tuesday.
BC next hosts Clemson on Saturday.