Utseya sparked a remarkable collapse as he claimed the wickets of Quinton de Kock, Rilee Rossouw and David Miller before finishing with career-best figures of 5 for 36, but a last-wicket partnership of 36 carried South Africa to a total of 231 all out.
That proved ample when Ryan McLaren and Dale Steyn took three wickets apiece to bowl Zimbabwe out for 170 in 38.3 overs.