"We broke each other back and forth in the beginning of the first set, and she had a few opportunities in the beginning," Sharapova said. "But once I started being a little bit more aggressive I felt like I had an edge on her. Her game is never an easy one - she makes you hit so many balls, and she has such a great slice - but that's when she has time to do all that. I tried to take that away from her today.
"But she's a tough first round, that's for sure - no matter where she is in the rankings, she has experience, has a Grand Slam, likes those center court matches - she lives in those opportunities."
The No.3-seeded Radwanska needed a little bit longer but won by the same score, converting all five of her break chances en route to a 66-minute, 62 61 win over American wildcard Maria Sanchez.
"My opponent tonight wasn't playing just one shot - she can change up her game, hitting the ball very hard and then some spin, throwing in a kick serve - she can play really good tennis," Radwanska said after the match. "The first match at any tournament is always tough, but I think I played consistently from the beginning to the end and stuck to my game tonight. I'm happy to win through in two sets."
And on the conditions? "It's different when it's cold," she said. "The court is much slower and the ball doesn't really go anywhere, plus the wind makes it tricky. I had to be careful from the beginning - I warmed up more, wore more clothes than usual and just tried to be warm from the beginning."
Next for Radwanska will be No.27 seed Sorana Cirstea - Radwanska won their last WTA meeting handily, coincidentally at Indian Wells last year, but Cirstea does have two wins in their five meetings.
"Well we've known each other for so long and we've played a couple of times against each other in the last few months, actually we played at Fed Cup zonals in February," Radwanska said of the match-up. "It's always a tough match against her, she can really hit the ball hard and she is a very powerful player, so I need to be focused from the beginning and try not to play too easy to the middle."
Other winners later on were No.9 seed Marion Bartoli, who beat Chanelle Scheepers, 63 63; No.19 seed Klara Zakopalova, who beat Shahar Peer, 67(2) 62 63; No.25 seed Carla Suárez Navarro, who beat Sílvia Soler-Espinosa, 61 61; Lara Arruabarrena-Vecino, who upset No.22 seed Varvara Lepchenko, 61 64; and qualifier Mallory Burdette, who beat No.23 seed Tamira Paszek, 76(0) 61.
Bartoli was happy to move through in straights. "I think I played solid and consistent tonight," she said. "Obviously Chanelle can play very well from the baseline and she likes my pace of ball, and it was chilly today, so I did pretty well to win, and getting it done in two sets was even better, as well.
"You never know what's going to happen in a third set, so I'm happy with my performance today."