In a contest that ebbed and flowed throughout, top seed and defending champion Kuznetsova harnessed the home crowd support to eventually triumph, 7-5, 6-7(2), 6-2, after a fraction over two and half hours on court.
The result keeps alive the 31-year-old's hopes of appearing at the BNP Paribas WTA Finals Singapore presented by SC Global. The Russian, who was a fixture at the season-ending showpiece for much of her early 20s, has not qualified since 2009, but will return should she lift the title in Moscow. If she fails in her quest, Johanna Konta will take the final spot in the eight-player draw.
Babos' battling performance ensured that the outcome remained in the balance until the last. In the second set, she displayed particular character to break twice with her opponent serving for the match. A flawless tie-break ensured the match went the distance, and despite falling behind in the decider, another comeback looked on the cards when she reduced her arrears to 3-2.
However, a thigh injury halted this revival - and the match - allowing Kuznetsova to regroup during a lengthy injury timeout. On the resumption, the Russian took control rattling off the final three games to set up a semifinal with No.4 seed Elina Svitolina.
"Where to start? My coach and Nastia [Myskina] said in the locker room that the points were very short, from one to three rallies. I didn't run much. I think I was good for me that I had a third set even when I felt a little bit tired," Kuznetsova told the Russian press. "In the third set I let the situation go and played better.
"It has prepared me a base for tomorrow's match because the way I played during last two matches, the last four sets: yesterday's and the first two from today?It won't get me far."
Earlier in the day, Svitolina delivered a clinical display to swat aside lucky loser Ana Konjuh, 6-1, 6-1. Svitolina has been in terrific form during the second half of the season, reaching the semifinals or better in three of her past five tournaments.
"It was a good match for me, I was serving well and seeing the ball good. This was a good game and I'm really happy that it's another semifinal for me," Svitolina told wtatennis.com.
"After Beijing I had one week off and I was at home, just trying to recover fast. These last two tournaments - here and in Zhuhai - are very important and I'm just trying to stay focused."