This was the first victory ever for the Blazers over the Golden Bears in seven meetings.
Elms (4-3) led 35-31 at halftime and by 16 at 58-42 following a three-pointer by junior guard John Ancrum (Harlem, NY) with 12 minutes left in the game.
Western New England College (2-5) rallied tying the contest at 67-67 on a lay-up by junior forward Peter Stathakis (North Attleboro, MA) with 2:43 remaining.
Branyon put the Blazers ahead 71-69 on a jumper at the 1:38 mark before senior guard Jon Godbout (Bristol, CT) made two free throws for the Golden Bears 19 seconds later to tie the game for the final time.
Sophomore forward Nathan Hawes (New Hope, MN) put Elms ahead for good with a free throw with 44 seconds left before Branyon sealed the victory with his three charity tosses.
Ancrum finished with 16 points while junior guard David Williams (Hartford, CT) had 24 points and eight rebounds. Freshman forward Antoine Holder (Hartford, CT) contributed 11 points.
Godbout led the Golden Bears with 20 points and dished out six assists. Stathakis played his best game ever finishing with a career high 15 points coming off the bench (making 6-of-7 shots from the field). Senior guard Jeremy Sternstein (Ithaca, NY) had 10 points.
Western New England College shot 54.5% from the field, but lost the battle of the boards 39-28 as the Blazers grabbed 22 offensive rebounds. Elms shot 36.2% from the field.