The Cardinals missed their first 11 shots before Reid's basket on three-point play on a post move gave them their first field goal nearly six minutes into the game. It was the first time in five games that Louisville trailed.
"We started out flat and it took us about 5 minutes to get in there and get energy going," said Louisville forward Sara Hammond, who finished with eight points and seven rebounds.
Louisville coach Jeff Walz attributed his team's slow start to recent road trips. The Cardinals won three games in the Puerto Vallarta, Mexico Nov. 20-22 to win the Hardwood Tournament of Hope before Monday's 79-61 win at Tennesee-Martin.
"We're a tired group," Walz said. "When you go back and look at our travel schedule, it's been a little crazy."
The Cardinals' defense sparked the first-half rally, scoring 22 points off 17 turnovers and holding EKU to just 14 percent shooting. It was the fifth time Louisville has held an opponent under 50 points this season.
EKU turned the ball over just the seven times in the second half and the Cardinals only outscored the Colonels 37-31 after the break. Barber's layup at with 13:33 remaining cut Louisville's lead to 46-25, the closest margin in the second half.
EKU lost its third straight after dropping games against Florida State and Wisconsin-Milwaukee in the San Juan Shootout in Puerto Rico during the Thanksgiving week.
Louisville's win comes before an in-state matchup of top 10 teams as No. 9 Kentucky visits on Sunday. It will be highest ranking in series history after the Cardinals were 10th and the Wildcats No. 12 last year when Kentucky won 74-54 in Lexington.
Hammond called the Louisville-Kentucky basketball rivalry the best in college sports.
"You all have seen in men's basketball how intense it is. It's just the same in women's basketball," she said. "We're two top 10 teams — just like the men are — so it's going it's going to be a battle."