The Australian hit 31 winners and broke the Russian four times in the one hour 28 minute match. She also won her eighth straight match at a major, having claimed the Wimbledon title a month ago.
Barty works hard to claim opening-round victory
After an opening hold to 15, Barty broke on her first chance with a stinging forehand winner to take a 2-0 lead. A subsequent hold to 15 extended her advantage to 3-0.
Zvonareva would get on the board in the next game, but the next time she served, she essentially broke herself following a double fault. Leading 5-1, Barty came through a tough 12-point game, saving a pair of break points to hold and clinch the set.
After trading breaks in the second set, the world number one seemingly took command, a stinging crosscourt forehand winner giving her another break and a 4-3 advantage. She held and moved one game away from victory.
Serving for the match at 5-4, Barty was surprisingly broken and the set would go to a tiebreaker. The Aussie held a 5-3 edge in the breaker, but again the Russian battled back and held a set point of her own at 7-6.
An off forehand winner got her even at 7-7. A magnificent touch volley brought up a second match point. And she converted after pummeling Zvonareva from corner to corner until she finally went long on a backhand.