Davidson's De'Mon Brooks threw the ball away with 6.7 seconds left and a one-point lead, and Marquette was given a final shot. Jamil Wilson inbounded the ball to Blue near midcourt with five seconds remaining, and Blue drove all the way to the basket on Davidson's Jake Cohen.
Blue, a 6-foot-4 guard, went to his left and got the ball off the backboard just over Cohen, who is 6-10.
Davidson (26-8) had won 17 games in a row, which was the longest active winning streak in the country.
Blue hit a 3-pointer with 28 seconds left to bring Marquette within two points, but Nik Cochran answered with two free throws for the Wildcats.
The Wildcats took an early 12-2 lead but allowed Marquette back in the game to take a 20-19 lead. From that point on—about five minutes remained in the first half at that point—until about the 10-minute mark in the second half, neither team could make a run. Whether it was on account of good team defense or poor execution and shooting on offense is debatable; either way, neither Marquette nor Davidson could make shots.
Throughout the drought it was Cohen who became the lifeblood of the Wildcats' offense. He struggled from the floor in the first half—his advanced post game was still giving him opportunities, the shots just weren't falling—but his persistence paid off in the second half.
He scored four points for Davidson in what was the biggest run for the Wildcats, a 10-2 stretch that gave them a 49-40 lead with 6:26 to play.
Cohen finished with a team-high 20 points.
For most of the game, Marquette (25-7) was unable to take advantage of the athleticism advantage it had over Davidson; the Golden Eagles out-rebounded Davidson, 41-29, but couldn't convert those rebounds into points. Marquette finished 34.6 percent from the floor (20-of-58), shooting its worst since it went 19-of-53 (35.8 percent) in a 70-51 loss to Louisville on Feb. 3.
The Golden Eagles' shooting woes reflected those of their two top scorers, Wilson and Blue. They had a combined 30 points points but shot a combined 9-of-28 from the floor.
Marquette will next play No. 6 Butler on Saturday.
NOTES: Marquette was in danger of being eliminated in the round of 64 for the first time since 2010, when it lost as a No. 6 seed to Washington 80-78. ... No. 3 seeds are 97-16 in the round-of-64 matchups since the field expanded 64 teams in 1985. ... Davidson has not won an NCAA tournament game since 2008, when Stephen Curry led the Wildcats to the Elite Eight. Before 2008, Davidson's last NCAA tournament victory was in 1969. ... Davidson has played in seven NCAA tournaments under coach Bob McKillop, who is in his 24th year on the Wildcats' sideline.