Bulldog sophomore guard Kellen Dunham finished with 18 points and a pair of rebounds to pace the winners.
"We had to come back in the second half of the game," first-year Butler coach Brandon Miller said. "I thought our team defense in the second half was the story of the game."
Trailing by as many as 12 in the second half, the Bulldogs began their rally on a key 3-point jumper from freshman guard Elijah Brown early in the second period, and gained their first lead of the half on a basket from Dunham with 4:05 remaining in regulation.
After the Bulldogs led by as many as four in the closing minutes, Marquette (10-8, 2-3) pulled within two on a dunk from forward Jamil Wilson and tied the game on a pair of free throws from guard Jake Thomas with five seconds left in the second half, forcing overtime.
The Bulldogs opened the extra period on two quick baskets from Dunham and junior forward Kameron Woods, who had nine points and six rebounds in overtime alone. Butler outscored the Golden Eagles 20-8 in the extra period, and shot 12 of 15 from the free throw line to seal the win.
Woods finished with 14 rebounds, tying a career-high, and 16 points, marking his fifth double-double of the season and ninth double-double of his career. The performance also marks Woods' fourth game in a row in double-digit rebounding.
"Our ability to get stops, our ability to get first-time rebounds, I'm extremely happy for our guys," Miller said. "I'm proud of our guys and their ability to execute on that end of the floor, especially at the end of the game, and especially in crunch time."
The Bulldogs were boosted by performances from senior forward Khyle Marshall, who also finished with 18 points, and senior forward Erik Fromm, who added 8 points on 2-4 shooting from 3-point range. Junior guard Alex Barlow also added 4 steals for Butler.
The win marks Butler's sixth overtime game of the season, inching closer to the school record for overtime games in a season from 1996-97, when the Bulldogs saw seven extra period games.
The Bulldogs will travel to Providence on Tuesday.