It was just North Carolina's 18th nonconference defeat in the 35-year history of the Dean E. Smith Center.
North Carolina scored first but did not lead the rest of the way as Marquette answered with a 14-2 run. Garcia had 16 points in the first half and Greg Elliott added 13 as the Golden Eagles led 45-29.
Marquette struggled in the backcourt against North Carolina's pressure defense in the second half, having 10 turnovers to just nine made field goals with 5:22 remaining. But the Golden Eagles went on an 8-0 run, with six points from Carton, for a 79-63 lead with 2:38 left to seal it.
Elliott scored 15 points with four steals and Theo John had 11 for Marquette (11-12). The Golden Eagles, who are currently 10th in the 11 team Big East, entered having lost six of their last eight - with two victories over Butler.
Garrison Brooks led North Carolina (14-8) with 18 points. R.J. Davis added 11 points, Walker Kessler scored 10, and Day'Ron Sharpe had nine points and 11 boards.
North Carolina is schedule to host No. 11 Florida State, looking for coach Roy Williams' 900th career victory. His 899 wins are third most all-time, behind Mike Krzyzewski (1,168), Jim Boeheim (977) and Bob Knight (902) -- all Naismith Hall of Famers. Legendary UNC coach Dean Smith won 879 games.
The Tar Heels had postponed home games against Clemson (Jan. 9) and No. 16 Virginia Tech (Feb. 16), along with Tuesday's road game at Boston College, amid COVID-19 issues involving their opponents.
Theo John makes a layup, dunks it down for Marquette
Theo John finishes with a layup vs. North Carolina and later scores a dunk for Marquette in the first half.