Palacios added seven rebounds, and Garcia had five assists for the Cardinals (12-3, 1-1 Conference USA), who scored 22 points off 23 TCU turnovers.
The injury-depleted Cardinals were coming off a 70-67 loss at Houston on Wednesday and Pitino sensed his team's morale was low.
After practice Friday, Wayne Cook, a motivational speaker who has cerebral palsy, spoke to the team.
"We really needed it," Pitino said. "It was a great lesson for our guys. We've been feeling sorry for ourselves and this really helped."
The players said the speech made a deep impact.
"Everybody kind of appreciated life a little more," said Garcia.
The Horned Frogs appeared to be the team with the shaken confidence Saturday.
The Cardinals jumped out to a 17-2 lead as the Horned Frogs had 11 turnovers in the first 9 minutes. Three minutes later, TCU had 14 turnovers and trailed 24-7.
"Where we had our problem was that they were way better defensively than we were offensively," TCU coach Neil Dougherty said. "They just took us out of a lot of things."
TCU's early sloppiness set aside Pitino's concerns about starting point guard Taquan Dean, who's coped with back spasms all week.
Sophomore Brandon Jenkins made his second start of the season in Dean's place. But Dean came off the bench and was often on the floor with Jenkins.
Dean had nine points and three assists in 26 minutes and Jenkins had five points, two assists and eight rebounds in 30 minutes.
Pitino said Jenkins was the most valuable player of the game - more for his defense than his offense. Jenkins had three steals and limited Corey Santee, TCU's leading scorer, to 13 points on 5-of-15 shooting.
"I told him in the locker room, 'You were the key to the game,"' Pitino said. "His pressure was relentless."
The Horned Frogs committed only one turnover in the final eight minutes of the opening half, but Garcia and Palacios made sure the Cardinals kept their comfortable lead.
The duo scored 28 of Louisville's first 34 points, with the 6-foot-7 Garcia either creating shots off his dribble or passing out of double-teams to the 6-8 Palacios, who was routinely open behind the 3-point line.
Garcia, from the Dominican Republic, and Palacios, from Colombia, flustered the Horned Frogs even more by using Spanish to communicate.
"It's great to play with him," said Palacios, who finished 8-of-12 from the field. "One time, I'm like, 'Pass the ball, man. You're going to score more than me.' We've got a good connection."
Palacios sank three 3-pointers and had 15 points in the first half; Garcia went 6-for-6 from the free-throw line and had 13 points in the opening 20 minutes.
Aaron Curtis scored underneath with 14:28 left in the second half to cut Louisville's lead to 11 and prompt a timeout from Pitino. The Cardinals responded with a 10-0 run and Larry O'Bannon's third 3-pointer pushed the lead to 61-40 with 10:59 remaining.
Pitino started pulling his starters near the 5-minute mark and the bench was all smiles - even Dean, who stretched out on the floor when he left the game.
"We were ready to get after it and that was a good thing to see," Dean said. "after that loss (to Houston), we could've easily hung our heads."
Nile Murry had 15 points and eight rebounds for TCU (10-5, 0-1), which had a four-game winning streak snapped.
TCU dropped to 1-46 in road games against Top 25 opponents.