The Bulldogs played without second-leading scorer and rebounder Andrew Smith, who was sidelined with an abdominal injury. They shot just 39 percent for the game and trailed by as many as 10 points late in the second half.
"The right team won," Butler coach Brad Stevens said in a release.
"I knew Charlotte coming in was going to be really hard for us to match up with, in large part because their strengths are certainly something that we counter better with Andrew (Smith) than without him," Stevens said. "That being said, we had opportunities and we didn't take advantage of them."
Butler (20-5, 7-3 Atlantic 10 Conference) hit just 11 of 33 shots in the first half and trailed 29-27 at halftime. Leading scorer Rotnei Clarke was held to just three points on one of six shooting in the opening 20 minutes.
The 49ers (18-6, 6-4), who shot 57 percent from the field in the first period, continued to build on their advantage behind a strong inside game in the second half. Henry hit a jump shot with 4:26 remaining to give the visitors a 59-49 advantage and the lead remained at ten points with under four minutes left.
That's when Clarke heated up.
The 6-foot guard, who entered the game as the fourth-leading scorer in the league, scored 15 points in the final 3:21 and gave the Bulldogs a chance to salvage the outcome. His fifth three-pointer of the game with nine seconds remaining drew the Bulldogs to within 68-67.
Butler quickly fouled Henry with seven seconds left, and the Charlotte guard hit one of two free throw attempts. Butler pushed the ball up-court and called a timeout with three seconds left. But the 49ers came up with a steal on the in-bounds play and E. Victor Nickerson closed out the scoring with a pair of free throws.
"If (the ball) would have landed in Rotnei's hands, I probably would have let it play out," Stevens said of the last sequence. "I don't like to take timeouts; I like the situation where their defense isn't set."
Clarke led all players with 18 points, while sophomore Roosevelt Jones added 17 points and nine rebounds.
Junior forward Erik Fromm, who was given a starting assignment, chipped in with a season-high 13 points and a career-high nine rebounds, while freshman Kellen Dunham had 12 points.
But the Bulldogs had zero points and just six rebounds off the bench.
"I didn't think we had a lot of guys play their best, and sometimes when you've got a guy out, you've got to rise up and do what you do well," Stevens said. "You don't have to do anything more than that, but you have to do what you do well."
Butler will travel to Fordham on Saturday at 4 p.m.