The 24-year-old was on hand to finish off Joe Ralls's delivery into the box with just eight minutes left of the match at the Cardiff City Stadium.
A tense game between two sides fighting for promotion yielded few moments of note in the opening 45 minutes.
The breakthrough was made when a Robins defensive mistake was pounced upon by Ralls, who was able to get behind the visitors' defence and whip a cross into the box.
Zohore was the intended recipient and the substitute made no mistake in firing into the net from five yards out to give the Bluebirds a fourth consecutive win.
The result sees Cardiff tighten their grip on second place in the Championship table, while Bristol City remain sixth in the standings.
CARDIFF CITY(4-2-3-1): Etheridge; Connolly, Manga, Bamba, Bennett; Halford, Ralls; Feeney (Harris 73'), Paterson, Hoilett; Madine (Zohore 45')
BRISTOL CITY (4-4-1-1): Fielding; Wright, Flint, Baker (Kent 85'), Magnusson; Brownhill, Reid, Smith, Bryan; Diedhiou (Walsh 85'), Diony (Paterson 69')