Yuki, now ranked 142, outclassed his opponent from Chinese Taipei 6-3 6-1 in the second round of the USD 50,000 hard court event while Prajnesh dispatched Australia's Marc Polmans 6-4 6-2 in his opener.
Carrying forward his unbeaten record against Chen, Yuki recorded his fourth straight win over the Taipei player in as many meetings on the Pro Circuit. He first beat him in Shanghai in 2014. Every year since then, Yuki has beaten the 34-year-old at least once in a season.
He next faces the Australian eighth seed John Millman, who dispatched Frenchman Antoine Escoffier 6-1 6-4.
Prajnesh will lock horns with top American Taylor Fritz, who knocked out India's Vijay Sundar Prashanth.
Among other Indians who made early exit from the singles event were Sumit Nagal and Saketh Myneni.
In the doubles, Myneni and Prashanth upset fourth seeded Peter Polansky and Akira Santillan 6-7(4) 6-2 10-8 to progress to the quarterfinals. Nagal is also playing doubles and has teamed up with local lad Nam Hoang LY.