Radwanska was in full control on center court at the Olympic Stadium until she led 5-1 in the second set. Dechy won the next two games and appeared to be turning the match, but the Pole broke her opponent for the win.
Barbora Zahalova Strycova of the Czech Republic beat Petra Cetkovska 6-4, 6-7 (2), 6-4, and Cetkovska then refused to shake hands.
Zahalova Strycova protested several calls in the match. Down 3-0 in the third set, she called for medical attention and a massage. After the interruption, she turned the match around and won the last set.
Zahalova Strycova will meet fifth-seeded Anabel Medina Garrigues of Spain in the second round. Medina Garrigues beat Swedish wild card Sandra Roma 6-3, 6-1.
Katarina Srebotnik of Slovenia also advanced to the second round, beating Anna Lapushchenkova of Russia 6-2, 6-1, while No. 4 seed Caroline Wozniacki of Denmark had to work hard to overcome Germany's Angelique Kerber 6-3, 6-4.
Wozniacki faces Finland's Emma Laine in the second round.
Swede Johanna Larsson delighted the home crowd when she rallied from a set down to beat Julia Goerges 3-6, 7-6 (5), 6-4.