A deep run in the Chinese capital will boost the Briton's chances of qualifying for the BNP Paribas WTA Finals Singapore presented by SC Global and also making her Top 10 debut.
However, she made an inauspicious start as Babos bossed the baseline exchanges to build an early lead. Roused from her slumber by this setback, Konta responded brilliantly, rattling off 13 of the next 16 games to close out a 7-5, 6-2 victory.
"I think I'm most pleased with coming through a match like that. I think both of us were struggling to find our level out there," Konta said. "Definitely when there's been a rain delay and a day of play has been missed it does break up the rhythm a little bit.
"I think that showed in both our tennis out there. So it was just about who could compete a little bit better and I was fortunate I was able to find that little bit extra and come through that."
Having dragged herself back into the match, the first set hinged on the 11th game. A wonderful instinctive volley earned Konta a break point, which she converted by whipping a forehand into the open court. She served out the set to love, going on to dominate the remainder of the match and book a date with No.5 seed Karolina Pliskova.
? Times Sport (@TimesSport) 5 October 2016
Currently No.14 in the rankings, Konta came close to breaking the Top 10 in the summer. She trails current No.10 Carla Suárez Navarro by 495 points and will likely need to make the final to join Virginia Wade, Sue Barker and Jo Durie as the only Britons to achieve the feat.
Her next challenge comes in the shape of recent US Open finalist Pliskova. On Tuesday, Pliskova was confirmed as the latest Singapore qualifier, however, her second-round opponent Daria Kasatkina very nearly spoiled the party, holding a match point before eventually going down, 3-6, 7-5, 7-6(7).