The No.6-seeded Bouchard was the first to take center court and succumbed to an on-fire Timea Babos, who broke once per set and fended off all five break points she faced to prevail, 6-4, 6-4.
"Genie's a great player, and she definitely has more confidence and is playing a lot better than the couple months before, so I'm happy I was solid and managed the tough situations well," Babos said.
And what about the big serving in those tough situations? "In general, in my game, I have one of the biggest serves on the tour, so it's a huge advantage for me, definitely. Genie is an aggressive player and takes the return very early - she has great returns - so I had to put a lot of first serves in.
"Thankfully in the big moments I came up with good serves and aces, so it worked out well."
The No.1-seeded Radwanska took the court straight afterwards and needed just 63 minutes to beat Wang Qiang, 6-3, 6-2, holding all nine of her service games - she saved both break points she faced.
Radwanska has now won 20 of her last 24 matches - including eight in a row on Chinese soil.
"We actually played each other in Tianjin, and I think she played a much better match this time, but I really pushed myself to play my best tennis today," Radwanska said. "It was a good match for me."
Up next for the World No.5 is Anna-Lena Friedsam, who won a see-saw battle against Katerina Siniakova in the late match, 6-4, 2-6, 6-1. Radwanska beat Friedsam in the pair's only meeting.
Babos has beaten Riske in both previous meetings, including in Tianjin just a few months ago.
Always love playing in Asia. Fans are great! https://t.co/8CDUy4dBfp
? Aga Radwanska (@ARadwanska) January 6, 2016