Nebraska 12-13 overall and 2-9 in the Big 12, while Texas 17-8 overall and 6-5 in the league.
"I thought we really competed hard and I am really proud of our players," Nebraska Coach Connie Yori said. "We really gave a great effort, we just made too many mistakes."
Moore hit a trio of three-pointers in the final 11 minutes and scored 13 in the second half to lead the Huskers back from a 21-point deficit with 7:34 left.
Although NU trailed big late in the second half, the Huskers trailed by just six at halftime, but UT's Yvonne Anderson scored 15 of her 17 in the second half to help the Longhorns build the lead.
Jordan Hooper added 12 points and eight rebounds for the Huskers, while Katya Leick also provided a lift off the bench with nine points and six boards. Leick's putback with 2:47 left cut the Texas lead to nine points, but Texas scored the game's final three points to seal the win.
Chassidy Fussell, who hit a pair of free throws to stop NU's late surge, also finished with 17 points, while Kathleen Nash added 10 points for UT.
For the game, Nebraska hit 40.4 percent (23-57) from the field, including 6-of-18 from three-point range. NU hit 14-of-29 shots in the second half, including 4-of-9 threes. NU outrebounded UT, 37-35, but lost the turnover battle, 25-15.
Texas scored 28 points off NU's turnovers, while Nebraska managed just 11 off UT's miscues.
Texas hit 45 percent (27-60) of its shots for the game, but connected on just 4-of-16 threes. UT did outscore NU, 9-3 at the free throw line.
The Huskers went to the locker room trailing 27-21, despite first-half foul trouble from Hooper and Catheryn Redmon. NU was tied with UT at 17 after a three-pointer from Jessica Periago with 5:48 to play, before Redmon picked up her second foul with 5:18 left in the half.
Down the stretch, Texas outscored NU 10-4 with six points coming from Nash, who had 10 first-half points. Fussell pitched in nine first-half points, including UT's lone three-pointer.
Moore and Leick each scored five first-half points, while Redmon added four first-half points.
NU hit 32.1 percent (9-28) of its first-half shots, including 2-of-9 three-pointers. The Huskers were 1-of-2 at the line and outrebounded Texas, 20-19. The Huskers committed 13 first-half turnovers, which resulted in 13 points for the Longhorns. NU did force eight first-half miscues, but the Huskers converted them to just four points.
Texas hit 36.7 percent (11-30) of its first-half shots, including just 1-of-6 three-pointers. The Longhorns were 4-for-4 at the foul line.
Nebraska returns home to take on Kansas State on Saturday at the Devaney Center. Tip-off between the Huskers and Wildcats is set for 7:05 p.m., and the game will be Nebraska's annual WBCA Pink Zone contest to promote cancer awareness. Live television coverage will be provided on Fox Sports Midwest in Nebraska.