The Heat trailed by as many as 14 in the fourth quarter before Bosh helped Miami stage a final surge.
His 3-pointers came during a 79-second span and were part of a stretch in which he supplied 13 straight Heat points.
LeBron James went 4-of-4 from the free-throw line in the closing seconds.
Bosh ended with 22 points and James put in 26 as Miami bested the Bobcats for a 14th consecutive time.
Kemba Walker provided 27 points and six assists for Charlotte.
Al Jefferson contributed 16 points and 13 rebounds.