Joel Berry II added 15 points for the Tar Heels (2-0), who led all the way to win their 14th consecutive home opener. But UNC followed its 24-point win over Temple in Friday's opener with an unimpressive showing full of missed free throws and leaky defense.
The Tar Heels struggled to put away a team that went 7-24 last season, a performance that had Hall of Fame coach Roy Williams burn a first-half timeout and let his team have it during an animated stoppage.
UNC led 40-32 at halftime and didn't put the game away until the final 10 minutes against the Stags (0-2), who hit 10 3-pointers that kept them hanging around longer than expected.
The Tar Heels are playing without preseason Atlantic Coast Conference co-player of the year Marcus Paige for the first few weeks of the season due to a broken right hand, so the play of Britt and Berry along the perimeter in Paige's absence at least offered some positives for the Tar Heels.
Britt, a junior, finished 6 for 9 from the field and tied his career high by making 4 of 6 3-point attempts, while Berry added three 3s while taking the bulk of the point guard duties with Paige out.
Brice Johnson scored 16 points as UNC had five players in double figures and shot 50 percent, though the Tar Heels made just 18 of 32 foul shots.
Marcus Gilbert scored 25 points to lead Fairfield before fouling out in the final minutes.
The game was part of the Naismith Memorial Hall of Fame Classic, though it wasn't part of the event's elimination rounds.
Fairfield: The Stags shot 35 percent for the game. ... Fairfield committed 19 turnovers, helping the Tar Heels to a 22-0 edge in points off turnovers. ... Freshman Jonathan Kasibabu had 10 rebounds.
UNC: Sophomore Theo Pinson finished with 11 points, five rebounds and eight assists in his second straight start. ... Fellow sophomore Justin Jackson had 11 points. ... Kennedy Meeks had 12 rebounds, while Johnson grabbed 11. ... UNC shot 55 percent in the second half.
North Carolina: Hosts Wofford on Wednesday.