Howard's spurt ended a 19-7 quarter-opening run by Marquette (20-13). The Golden Eagles, who received an at-large bid to the NIT and are the second seed in the Notre Dame quadrant, will host third-seeded Oregon in the second round on Sunday at 4:30 p.m. ET.
Seventh-seeded Harvard, which received an automatic bid to the NIT by winning the Ivy League regular-season championship, finishes 18-14.
Howard finished with 22 points while Andrew Rowsey scored 15 points and Jamal Cain added 11 points for Marquette.
Justin Bassey scored a career-high 19 points, including 13 in the fourth quarter, and added a team-high 12 rebounds and five assists for Harvard. Corey Johnson added 10 points.
Harvard appeared buried when Marquette scored the first seven points of the fourth quarter to extend its lead to 53-34, but the Crimson mounted an 18-7 run and pulled within single digits on Rio Haskett's 3-pointer with 3:17 remaining.
Harvard could have pulled within a single possession in the final minute, during which Marquette turned the ball over on three straight possessions. Bassey converted the first turnover into a layup to close the gap to 63-57, but he missed two free throws following the second turnover and threw the ball away after the third turnover.
Howard and Rowsey combined to hit all four of their free throws over the final 19 seconds for Marquette, which went 18 of 19 from the line. The Crimson hit 9 of 17 foul shots.
Both teams struggled offensively in the first half, which ended with Marquette holding a 27-21 lead. Harvard endured three scoreless droughts of at least three minutes apiece while the Golden Eagles opened the second quarter by missing their first five shots, a span in which the Crimson went on a 7-0 run to take their last lead.
--Field Level Media
Harvard | Marquette | |
Justin Bassey 19 | Scoring | Markus Howard 22 |
Justin Bassey 5 | Assists | Andrew Rowsey 6 |
Justin Bassey 12 | Rebounds | Matt Heldt 8 |
Justin Bassey 3 | Free Throws Made | Markus Howard 9 |
Justin Bassey 4 | Steals | Jamal Cain 3 |
Chris Lewis 1 | Blocks | Matt Heldt 3 |