McCoughtry, the Big East's leading scorer at almost 24 points, came in averaging just 13 points in three NCAA tournament games. She had 14 at halftime in this one.
"I felt like I played one of my worst games of my career tonight," McCoughtry said. "But we got some runs and we got some layups and I think that helped."
Chauntise Wright led Louisville (25-9) with 21 and seven rebounds, and Patrika Barlow had 11 assists and seven rebounds. Louisville advances to play Kansas State Tuesday in the second round of the New Orleans regional. The Wildcats beat Chattagnooga 69-59 earlier Sunday.
"We survived tonight," Louisville coach Jeff Walz said. "It was not very pretty, that's for sure."
Amanda Jackson led all scorers with 22 points, 16 in the second half for the 13th-seeded RedHawks (23-11), champions of the Mid-American Conference.
They outrebounded Louisville 38-32, and had 25 offensive boards, while forcing 25 turnovers.
Louisville led by as many as 15 in the first half, but Miami cut it to 49-41 just over five minutes into the second half.
A 3-pointer from Jackson made it 58-49 with just over 9 minutes left.
But Brandie Radde answered with two 3-pointers and Candyce Bingham added a three-point play to stretch the lead back to 67-49, and the Cardinals were never again threatened.
"I knew, being wide open and my seniors telling me to shoot the ball I had to knock that down," Radde said. "Then I came back down and hit another one, and just stopped their run, started a little run of our own."
McCoughtry left the game with 4:39 after coming down on a teammates foot and rolling her left ankle. She stayed on the Cardinals bench for the rest of the game, but said she'll be ready to play on Tuesday.
Laura Markwood suffered a similar injury for Miami less than two minutes later. She had to be helped off the court, and finished with 13 points and eight rebounds.
Miami opened the scoring with a 3-pointer from Jenna Shone, before Louisville went into its pressure defense. McCoughtry hit a 3, and the Cardinals got two quick steals and buckets, forcing Miami into a timeout just 2 minutes into the game.
"That's how we wanted to start," Walz said. "We wanted to try to get up into them, defensively try to cause as many turnovers as we could and Angel is a big part of that."
McCoughtry had 12 of the Cardinals first 18 points, and helped Louisville to an early 24-11 lead.
The RedHawks responded with an 8-0 run as Shone broke the press, leading to several easy buckets in transition.
But Miami had no real answer for 6-foot-3 Chauntise Wright, who used her size to get position inside on the smaller Hawks. She had 10 first-half points and McCoughtry had 16 as the Cardinals went into halftime up 41-28.
"I think my strength helped out a lot," Wright said. "There were sometimes when they were holding, and I just cut through them."
Jackson, Miami's all-time scoring leader, was held without a field goal for the first 16 minutes.
"In the second half, I was just more aggressive and letting the game come to me," Jackson said.
The RedHawks had won six straight and 12 of 13.