The Polish world number four had to dig deep in the year's first tournament to edge out the 70th-ranked American 7-6 7-6.
"I've never been in a final in my first tournament of the year, so it's a good start, and I'm going to do everything in my power to win that match tomorrow," Radwanska, who is yet to drop a set at the tournament, said.
"Winning a title is a great thing, especially at a tournament I haven't played before."
Third seed Wickmayer reached her third Auckland final in four years after winning a final set tie-break against eighth-seeded German Mona Barthel.
The 2010 champion and runner-up a year later won 6-4 1-6 7-6 after struggling against Barthel's serve in the windy conditions.
"It was really tough to get a rhythm on her serve - it's really tough to read, and when she served a bit slower the wind was taking it," the Belgian said of the Barthel serve, which produced 12 aces.
"I managed to stay mentally strong in the tie-break - I'm really happy with the way I handled that pressure."
WTA Brisbane results
3-Serena Williams (U.S.) beat 1-Victoria Azarenka (Belarus)WO
Anastasia Pavlyuchenkova (Russia) beat Lesia Tsurenko (Ukraine) 4-6 6-1 6-2
WTA Auckland results
1-Agnieszka Radwanska (Poland) beat Jamie Hampton (U.S.) 7-6(4) 7-6(3)
3-Yanina Wickmayer (Belgium) beat 8-Mona Barthel (Germany) 6-4 1-6 7-6(3)
WTA Shenzhen results
1-Li Na (China) beat 6-Peng Shuai (China) 6-4 6-0
5-Klara Zakopalova (Czech Republic) beat Monica Niculescu (Romania) 6-1 6-3