Lamont Mack added 12 points for the 49ers (11-5, 2-0), who led by as many as 14 points in the second half.
Pat Calathes scored 19 points, Garrett Williamson 12 and Darrin Govens 11 for the Hawks (9-5, 2-1).
Down 11 points with 9:07 remaining, Saint Joseph's went on a 12-1 run, with Williamson's layup with 3:47 left tying the score at 61.
The Hawks then led twice, the last at 64-63 on a pair of Williamson free throws with 1:29 left, but Goldwire hit a 3-pointer 15 seconds later to put Charlotte in the lead to stay.
The 49ers then hit 4-of-6 from the free throw line to seal the win and improve to 8-0 in games at Halton Arena.
Saint Joseph's played without starting point guard Tasheed Carr, the Atlantic 10's assists leader and Saint Joseph's No. 3 scorer. Carr sprained his right ankle during practice Monday, and did not make the trip.
Despite Carr's absence, the Hawks led by six points three times in the opening minutes of the first half, the last at 20-14 on Ahmad Nivins' dunk with 10:15 left.
But Goldwire scored 13 points during a 15-4 run - including 10 points over a 70-second span - that put Charlotte ahead en route to a 39-34 lead at the break.
Goldwire nailed a 3-pointer under pressure with 5:58 left to give the 49ers a 26-24 lead, then capped an 18-point first half with a 3-pointer to give the 49ers a 39-32 margin with 1:50 remaining, their biggest lead of the half.
