Winthrop didn't have an answer for Valeriy Berezhynska early when she sparked Rice to a 16-0 lead.
The Lady Eagles didn't have an answer in the end when she hit a 3-pointer with 17 seconds in regulation to tie the game at 52 after the Lady Eagles had staged an amazing comeback to take a 10-point lead.
And, more importantly, the Lady Eagles didn't have an answer in overtime when the 6-foot-4 powerhouse made crucial free throws and a steal to seal Rice's 63-54 victory in the final game of the Winthrop Classic.
Berezhynska, the three-day event's most valuable player, scored 31 points and pulled down 10 rebounds as the Owls improved to 3-0.
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"She schooled us early on," Winthrop coach Bud Childers said after the Lady Eagles lost for the first time. "Then we made it tougher on her. But give her credit, she stepped up and made the clutch shot."
After a miserable start -- Winthrop didn't score until the 13:18 mark -- the Lady Eagles started to peck away at the Owls' lead by running their offense, finding the range and toughening up defensively.
Slowly, the lead began to shrink, with Rice holding on to a precarious 30-26 lead at the break. Back-to-back baskets by Ashley Haugtvedt tied it with 18:51 left.
Berezhynska's short jumper put Rice back on top, but Winthrop would go on a run and built a 10-point cushion behind Yvonne Van Daalen and Franchesca Davenport, who ended the game with a team-high 15 points.
The game was close down the stretch, with Winthrop taking a 52-49 lead when all-tournament selection Ashley Fann hit a free throw with 36 seconds left.
Rice worked the ball around the perimeter looking for a 3-pointer. When nothing developed, Berezhynska stepped out and hit the trey.
Winthrop came up court and set up a play that had Van Daalen driving to the basket. Her shot rolled off the rim into Fann's hands, but her putback was just off.
Rice controlled the overtime.
"We played right to the finish," Childers said. "I don't know how much gas we had in the tank in overtime. I couldn't be more proud of our team. We played our hearts out."
Tiffany Rodd, who carried the Lady Eagles on Saturday, scored seven points and was named to the all-tournament team, along with Rice's Maudees Fowler and North Texas State's Amber Jackson.
• NORTH TEXAS 56, NAVY 45 -- Brittany James and Amber Jackson scored 16 points each and combined for all but 11 of their team's 35 second-half points to lift the Mean Green to its first win of the season.
Whitney Davidson had 10 for the Midshipmen, who drop to 0-3.