Rathan-Mayes scored a season-high 35 points and hit five 3-pointers to lead the Seminoles (10-10, 2-5), including three in the final 35 seconds to keep FSU in it all the way to the horn.
His last 3 brought the Seminoles to within 75-72 with about 17 seconds left, but FSU could get no closer.
Freshman Justin Jackson added 14 points in his latest solid performance as UNC won for the 10th time in 11 games.
Johnson finished 7-for-9 from the field to continue his hot shooting from Wednesday's win at Wake Forest and also had a couple of tough plays in the paint that coach Roy Williams has been pushing to see. Paige, leading an injury-depleted backcourt, went 6-for-13 from the field and also hit two free throws with 16.1 seconds left to help keep the Tar Heels in control after Rathan-Mayes' final 3.
UNC finished with four players in double figures and shot 48 percent. FSU relied almost entirely on Rathan-Mayes, who scored 22 second-half points and finished 14-for-26 from the field. No other Seminoles player hit more than four shots as the team finished at 44 percent shooting.
The Tar Heels knew they would be short-handed for this one after the latest in a line of backcourt injuries, this one freshman Theo Pinson's broken left foot suffered in Wednesday's win at Wake Forest.
They also weren't sure if they would have sophomore Nate Britt after he took 15 stitches for a cut lip after that game, though he played 14 minutes and scored four points.
FSU: This was FSU's ACC-high fifth league road game. ... The Seminoles haven't won in Chapel Hill since February 2010. ... Devon Bookert scored 11 as the only other FSU player to reach double figures. ... Rathan-Mayes scored the most points by a UNC opponent in the Smith Center since LaSalle's Lionel Simmons scored 37 in January 1988.
UNC: In addition to Pinson, the Tar Heels were again without guards Joel Berry II (groin), Stilman White (foot) and Luke Davis (foot) due to injuries. ... Former football coach Mack Brown, who spent 10 seasons here before taking over at Texas, attended the game and was recognized during a stoppage with the '90s song "Return of the Mack" by Mark Morrison.
UNC hosts Syracuse on Monday.