Tina Charles added 18 points, converting several clutch baskets inside over 6-foot-6 LSU center Sylvia Fowles.
Charles' last basket gave UConn (27-1) a 72-66 lead with a little over a minute to go.
Quianna Chaney hit her sixth 3-pointer of the game shortly after to pull LSU to 72-69. LSU (23-4) forced the Huskies into a shot clock violation, gaining a chance to tie the game on its next possession. Chaney, who finished with 22 points, rushed her next attempt, however, and the Lady Tigers were forced to foul with 6 seconds left.
Moore made them pay, hitting two free throws to put the game away.
Fowles finished with 26 points and 11 rebounds to lead LSU.
Kaili McLaren had 11 points and 12 rebounds and Renee Montgomery scored 10 points in a tense, physical game that sent players from both teams hard to the floor. At one point in the second half, Connecticut head coach Geno Auriemma launched into a tirade and was assessed a technical foul as he was held back by assistant coaches.
The game marked the second time in less than two weeks that LSU had faced a No. 1 team. The Lady Tigers were impressive in their first such opportunity, beating Tennessee by 16 points on Feb. 14.
LSU coach Van Chancellor called his team's contest against the Huskies the game of the year in women's college basketball.
Although these giants of the women's game don't play in the same conference, they have a history.
UConn pulled out a dramatic one-point victory in Baton Rouge last season, only to suffer one of its worst NCAA tournament losses to the Lady Tigers last spring.
NO. 2 NO. CAROLINA 85, N.C. STATE 79
In Chapel Hill, N.C., Erlana Larkins scored 18 points and North Carolina clinched a share of the Atlantic Coast Conference title by beating North Carolina State.
Jessica Breland and Rashanda McCants each added 16 points for the Tar Heels (26-2, 13-0), who went ahead to stay by outscoring N.C. State 20-10 during a 7-minute stretch that bridged halftime and withstood a late Wolfpack charge to secure their ninth straight victory.
INDIANA 69, NO. 18 OHIO STATE 61
In Bloomington, Ind., Jamie Braun scored 19 points, including two clinching free throws with 39 seconds left in overtime, to help Indiana beat Ohio State.
The Hoosiers (16-12, 9-7 Big Ten) snapped an eight-game losing streak to the Buckeyes (20-7, 11-5) and avenged a 71-59 loss at Columbus last month, when Braun scored a season-high 25 points.