Up two breaks, Radwanska served for the first set at 5-2 and had three set points but Wozniacki hung tough to win the game and eventually forced a tie-break, in which she never trailed. From there she cruised to a 76(4) 62 triumph.
"It was tough playing Urszula because she plays really flat, which works well on this surface, where the ball doesn't bounce very high," the top-seeded Wozniacki said. "I was able to serve well when I needed to and hope to serve even better in my next match.
"The first match is never easy and I am looking to improve with each one here."
Wozniacki, who grew up in nearby Odense, delighted the crowd by capturing the title at the first two editions of this event in 2010 and 2011. She is now 11-0 here and has won 15 straight sets. Next up for her is Pauline Parmentier.
"It was obviously a very difficult match, as you can see from the scoreline," Kerber said. "I thought both of us played really well. I tried to play my natural game, but in the first set she made it really tough for me to do that. However, I managed to get into the match more and play better as the match went on, and in the end I'm really happy I won and am through to the second round."
"The score suggests it was a comfortable match, but the start of both sets were very close and difficult," Niculescu said. "Once I got past that I managed to dictate a little more with my game. I'm happy to be through and am looking forward to my next match."
Other seeded winners were No.5 seed Kaia Kanepi and No.6 seed Mona Barthel. A stomach illness forced No.7 seed Ksenia Pervak to retire in the second set against qualifier Johanna Konta. No.8 seed Sofia Arvidsson was eliminated by Patricia Mayr-Achleitner, 75 57 61.
Among the unseeded winners, Alizé Cornet recorded her first career double bagel over Malou Ejdesgaard, only yielding 15 points in 42 minutes.