In game that featured nine ties and 13 lead changes, the Golden Eagles (4-0) rode the sharp shooting of Jones to squeeze past a Maryland team that had won its first three games by 30, 34 and 31 points, respectively.
Marquette led 74-66 with 1:07 left before the Terrapins charged back. It was 76-74 when Maryland's DeShawn Harris-Smith stepped to the foul line for two shots with 14.7 seconds remaining.
He missed both.
Jones went 10 for 18 from the floor and made three of his five attempts from beyond the arc.
Freshman center Derik Queen and Ja'Kobi Gillespie scored 24 points apiece for Maryland (3-1).
Stevie Mitchell chipped in with 18 points for the Golden Eagles in their first road game of the season.
Takeaways
Marquette: The Golden Eagles reached the Sweet 16 of the NCAA Tournament last season, but now they're without Tyler Kolek and Oso Ighodaro, both of whom are in the NBA. Jones has helped fill the void and Mitchell helped against the Terrapins, but depth is an issue.
Maryland: The Terrapins showed they can hang with a top-15 team, but this was a tough loss to take at home in a packed arena.
Key moment
Maryland led 61-59 before Jones drained a 3-pointer and followed a missed 3 by Queen with a three-point play that made it 65-61 with 6:11 remaining.
Key stat
Maryland committed 13 turnovers and went 9 of 14 from the foul line, including those two critical misses by Harris-Smith in the final minute. Marquette, in contrast, turned it over only seven times and was 18 for 24 on free throws.
Up next
Marquette: The Golden Eagles face another Big Ten opponent, No. 13 Purdue, at home on Tuesday night.