Semaj Christon added 18 points and five assists to help the fourth-seeded Musketeers (21-11) earn a matchup with 14th-ranked Creighton in Friday's semis, with Isaiah Philmore contributing 10 points to the win.
Xavier was able to move on by outperforming the Golden Eagles at the free throw line, hitting 17-of-23 foul shots compared to an 8-of-14 success rate for Marquette.
The Golden Eagles (17-15) were also hurt by turnovers, committing 15 giveaways that were turned into 15 Xavier points and which offset a 57.8 field goal percentage.
Deonte Burton netted a game-high 23 points on 9-of-14 shooting in the loss, with Todd Mayo finishing with 21 while going 8-of-13 from the field.
Xavier trailed 48-47 midway through the second half before forging ahead to stay behind a 10-3 run that Matt Stainbrook capped with a layup with 4:33 to go, putting the Muskeeters up by a 57-51 count.
Marquette closed within 59-58 on Jamil Wilson's bucket with 2:10 remaining, before four straight Martin free throws pushed the lead back to five with 49 seconds on the clock.
The Muskeeters were still up by five when Mayo buried a 3-pointer with 25 seconds left that cut Marquette's deficit to 65-63. Mayo missed from beyond the arc on the Golden Eagles' next possession, however, after Christon went 1- of-2 from the line to extend the lead back to three.
Christon came down with the rebound on Mayo's miss before sealing the win by again hitting one of his two bonus attempts.