The home side held a slim 19-16 lead at the break, but pulled away in the second half to secure a win in the final match of the opening weekend of the competition.
The match was the second of two of the Rugby Festival held at the BCM Stadium and the faithful were rewarded with a good win by the home side.
Border scored early in the match when winger Sipho Nofemele gathered his own kick ahead to score under the posts.
Zimbabwe answered with two penalty goals by Brendon Mandivenga, before a second try by Border opened the gap between the sides again. Scrumhalf Bangi Kobese was quick to respond with a tap penalty near the Zimbabwe tryline, catching the visitors’ defence napping.
A strong run by centre Riaan O'Neill set up Zimbabwe's first try in the competition, with flanker Brian Nyaude dotting down.
Mandivenga converted, but from the restart, his forwards dropped the ball and Border hooker Lubabalo Lento scored in the corner for the home side.
The second half was all Border.
Flyhalf Aphiwe Stemele opened the scoring with an early penalty goal before a well-worked line-out move saw Nofemele diving over in the corner for his second try.
Hard-working flanker Onke Dubase extended the lead with a well-deserved try before Stemele provided the final nail in the coffin with an intercept try under the posts.
Border 41 (19), Zimbabwe Academy 16 (16)
Border - Tries: Sipho Nofemele (2), Bangi Kobese, Lubabalo Lento, Onke Dubase, Aphiwe Stemele. Conversions: Aphiwe Stemele (4). Penalty goal: Stemele.
Zimbabwe Academy - Try: Brian Nyaude. Conversion: Brendon Mandivenga. Penalty goals: Mandivenga (3).