Neil Jenkins, playing at centre instead of outside-half, started the points rush with a fifth-minute penalty and then converted two tries, by the scrum-half Rupert Moon and the debutant wing Simon Hill.
After the Zimbabwe captain Dave Walters and Jenkins had exchanged penalties, Wales then dried up until their outside-half Adrian Davies dropped a goal with the last kick of the first half.
Walters kicked a second penalty at the start of the second half before the Llanelli wing Wayne Proctor squeezed over for the visitors' third try. Midway through the half, the Zimbabwe wing Victor Olonga pounced for his side's only try after the Cardiff full-back Mike Rayer had dropped a high ball from Craig Brown beneath his posts.
Even though Zimbabwe dominated the final quarter with Walters landing his third penalty, the Llanelli lock Phil Davies charged through for the fourth Welsh try seven minutes from time, and Jenkins again converted.
Zimbabwe: I Noble; D Nash, M Letcher, D Walters (capt), V Olonga; C Brown, S Day; G Snyder, B Beattie, A Garvey, R Demblon, T Tabvuma, S Landman, E Fargnoli, B Dawson.
WALES: M Rayer; S Hill (both Cardiff), R Bidgood (Newport), N Jenkins (Pontypridd), W Proctor (Llanelli); A Davies (Cardiff), R Moon (Llanelli); M Griffiths (Cardiff), A Lamerton (Llanelli), H Williams- Jones (S Wales Police), P Davies (Llanelli), G Llewellyn (Neath, capt), M Perego, E Lewis, L Jones. Replacements: N Boobyer (all Llanelli) for Proctor, 48 min; S Davies (Swansea) for Lewis, 77 min.
Referee: I Rogers (SA).
Scotland overcame driving rain to beat an inexperienced Fiji B side 14-7 in Nadi in the opening game of their Pacific tour yesterday. The visitors' points came via three penalties by Ally Donaldson and a try from John Kerr.