Yet Goestenkors said her team lacked focus and energy.
"I'm very disappointed with our focus and our energy," said Goestenkors, whose team turned the ball over 19 times. "We need to take care of the basketball better. There are no excuses for this type of play."
Beard led a 23-7 Duke run to open the second half, putting the game out of reach. She needs 51 points to break the school's career scoring record held by Chris Moreland with 2,232 points.
The Blue Devils (8-1) have won eight games in a row after losing their season opener to Texas. But they showed the effects of not playing for eight days and came out slow in the first half.
Trailing 15-14 with 10:07 left in the half, Duke went on a 19-2 run to take a 33-17 lead with 5:09 remaining in the half.
Goestenkors credited Beard and Duke's full-court press with turning the game around.
"Our full-court press did produce several easy baskets for us in the first half," Goestenkors said. "Alana ignited us with her defense."
Beard scored 14 points in the first half to lead Duke to a 46-30 halftime lead.
"We lacked focus," Beard said. "We have to take every game like it's a championship game."
Sharema Dean led Hampton (1-7) with 16 points. Kiesha Beard added 15 points and nine rebounds for the Lady Pirates.
Brittany Hunter , playing in her first game for Duke since knee surgery in November, scored 12 points and grabbed nine rebounds. Monique Currie added 12 points.
Iciss Tillis had 11 points and nine rebounds, and Lindsey Harding had eight assists for the Blue Devils.