Sabalenka was assured of replacing Iga Swiatek at the top of the women's rankings after the Polish No.1 crashed out of the US Open on Sunday.
However Sabalenka said she is not thinking about her new-found status as the world's top player just yet.
"Of course I'm happy ... it's incredible for me and my family
She played amazing tennis at the US Open this year, so I'm really delighted with the victory over her.
After Iga Swiatek, the current leader in the women's rankings from Poland, withdrew from the US Open on Sunday, Sabalenka seemed certain to take her place at the top.
Sabalenka asserted that she is not yet considering her newfound position as the best player in the world.
"Of course I'm happy. It's amazing for my family and I."
But I still have some work to do in New York this year, so I won't consider it until after the US Open.
After defeating last year's finalist Ons Jabeur in the fourth round to advance to her maiden Grand Slam quarterfinal, rising Chinese star Zheng had been daydreaming of pulling off another upset.
While Sabalenka, the 20-year-old 23rd seed, threatened to pull away with the match after a fast start in which she broke Zheng twice for a 3-0 lead while giving up only two points, the hard-hitting Sabalenka never seemed like she was going to be defeated.
Sabalenka served out easily to win the opening set in only 27 minutes, despite Zheng holding in the sixth game to make it 5-1. Zheng was broken once more to go 4-0 down..
Sabalenka's domination was demonstrated by her serve, where she won 13 of 19 and 23 of 26 points on her second serve. Throughout the entire match, Zheng was unable to create a single break point opportunity.
Although Zheng performed marginally better in the second set, Sabalenka's triumph was never in doubt once she broke in the seventh game to take a 4-3 lead. In the tenth game, she completed the victory on service.
