Radwanska hit some classic winners, and looked improved after her shaky three-set win over Beatriz Haddad Maia in the opening round.
The Polish fourth seed credited Townsend for a tight battle in the second set, which required a late Radwanska break to seal victory.
"It was a lot of up and downs, a lot of breaks but I still think it was a really good match. She came with some unbelievable shots in a couple of moments. She can be really tough and surprised me a couple of times. She could make those angles from pretty much every corner of the court.
"I'm feeling better and better each match and hopefully I can play better and better. Every match helps, so I am very happy I can play another match here."
The 2013 champion has still yet to lose a game in Auckland, and her latest victory booked a quarter-final berth against American qualifier Sachia Vickery.
9.50pm: Agnieszka Radwanska has taken control of the first set against Taylor Townsend in their second round encounter at the ASB Classic.
Radwanska has won the first set 6-3, undeterred by a 20 minute rain delay when leading 4-1.
Townsend had some deft touches and a powerful forehand but won none of her eight points on her second serve as Radwanska attacked the second offerings.
The American did manage to break back to extend the set, but Radwanska finished it off with her next service game to move one set away from the quarter-finals.
8.45pm: Julia Goerges has made light work of her second round match, easing into the ASB Classic quarter-finals with a 6-4, 6-0 victory over Slovakian qualifier Viktoria Kuzmova.
Goerges had struggled in the first round, needing three sets to beat Monica Puig, but she overwhelmed the 19-year-old Kuzmova, hitting nine aces and dominating on first serve to easily progress.
Goerges had earlier ground out a three-set victory over Monica Puig in her opening game, which finished at 1.21am, but she will enjoy her much earlier finish tonight, requiring just 65 minutes to progress.
I'm very happy to be in another quarter final here - I was happy with my serve," said Goerges, who was pleased to start the season 2-0.
"I can always improve what I am doing but I am very happy that I could win them both."
She will next play Slovenia's Polona Hercog, ranked 100th in the world.
5.55pm: Caroline Wozniacki's procession through the ASB Classic has continued.
After a 6-3 6-0 victory over Madison Brengle last night, Wozniacki has put in a strong second showing, beating Petra Martic 6-2 6-2.
Wozniacki, who remains the only seed yet to lose a set, took just 53 minutes to seal the victory, and continued the exquisite tennis she displayed last night as winners were blasted past Martic.
Wozniacki won 89 per cent of points on first serve, and Martic never threatened as the number one seed claimed a second consecutive comfortable victory at Stanley Street.
The Danish world number three has now made the quarter-finals on each of her four appearances in Auckland, but has yet to claim the title. This year, she has claimed clear favouritism, such is the ease of her victories, with neither win taking more than an hour.
She will play promising young American wildcard Sofia Kenin in the quarter-finals, after Kenin battled past Varvara Lepchenko 6-4, 7-6.
In the only match on centre court featuring unseeded players, Polona Hercog has defeated Kirsten Flipkens, comfortably prevailing 6-4, 6-2.
Sachia Vickery has also continued her impressive run, with the qualifier making the quarter-finals after a 6-4, 6-2 win over Veronica Cepede Royg.
3.05pm: Barbora Strycova is through to the quarter-finals at the ASB Classic, but it took longer than expected.
Up 6-1, 4-2, Strycova looked set for an easy progression into the next round, but opponent Johanna Larsson battled back, forcing Strycova to battle for nearly two and a half hours before eventually claiming a 6-1, 6-7, 6-2 victory.
It was another marathon effort on centre court for Strycova, who yesterday needed three hours to defeat Sara Errani, and her fitness has been tested early in the season.
However, once again she showed enough strength to come out on top in the third set, with her serve much more solid than in her win over Errani.
Larsson only had three break points, converting one to get back into the match in the second set, but was well outgunned in the first and third sets as Strycova toiled to a hard-fought victory.
The Czech world number 23 has now made the quarter-finals three times at the Classic, but has never made the final. That could change this year, with a relatively simple quarter-final draw seeing her play world number 103 Su-Wei Hsieh in the next round.
Hsieh beat Ysaline Bonaventure 6-4, 6-3, while American wildcard Sofia Kenin has taken the first set against Varvara Lepchenko, 6-4.
Caroline Wozniacki is next up on centre court, against world number 90 Petra Martic.
2.15pm: An unexpected third set at the ASB Classic.
Johanna Larsson has come from 6-1, 4-2 down to win the second set in a tiebreaker against Barbora Strycova, and send it to a decider.
Strycova looked set for an easy progession to the quarter-finals, but - like in her opening round against Sara Errani - she blew a chance to serve out the match in the second set.
Larsson took out the tiebreaker 7-3, performing much better on serve, and making it a second straight day where Strycova will be involved in a marathon match on centre court.
The winner will play world number 103 Su-Wei Hsieh in the next round.
1.10pm: Barbora Strycova has cruised through the first set of her second round clash at the ASB Classic.
Strycova has thrashed Johanna Larsson 6-1 in just 29 minutes on centre court, in a set which was one-sided from the first three points.
Larsson's play was as blinding as her fluro yellow outfit as she won no points on her second serve, being broken twice due to double faults.
Conversely, Strycova found her serve after struggling with it against Sara Errani, winning 91 per cent of points on her first serve to look on track for a spot in the quarter-finals.
12.15pm: Day three of the ASB Classic will see all the top four seeds in action on centre court.
After the other four seeds were bundled out in the first round, the biggest four names remain, but only Caroline Wozniacki looked convincing in her first round match, with the other three all requiring three tight sets to advance.
Third seed Barbora Strycova was one of them, needing three hours to grind past Sara Errani, and she is first on court against another familiar face, Sweden's Johanna Larsson.
Strycova has won four of the seven matches between the pair.
Wozniacki will follow that clash on centre court against world number 90 Petra Martic, while Kirsten Flipkens will play Polona Hercog in the only unseeded match on centre court.
On the outside courts, Ysaline Bonaventure will take on Su-Wei Hsieh for a spot in the quarter-finals, as will Sofia Kenin against Varvara Lepchenko. Sachia Vickery, who knocked out defending champion Lauren Davis yesterday, will clash with Paraguay's Veronica Cepede Royg.
In the night session, second seed Julia Goerges faces qualifier Viktoria Kuzmova, while Agnieszka Radwanska takes on Taylor Townsend in the final match of the night.
Rain threatens to briefly interrupt play this afternoon, but tournament organisers will be hoping to complete every game, with heavy downpours likely for all of Thursday's schedule.
