Blue also had one of two vital 3-point shots that helped the Golden Eagles overcome a late deficit. But it was his drive down the left side of the lane for a layup for the game's final points with 1 second left that completed the comeback.
Marquette (24-8) moves into an East Region third-round game against sixth-seeded Butler Saturday. Butler defeated Bucknell 68-56 in its second-round game earlier Thursday.
Davidson, which entered the game with the nation's longest winning streak at 17 games, completes its season 26-8.
The Wildcats led much of the game and were up by nine 49-40 when Jake Cohen made a jump shot with 6:27 to play. That, however, would be the last field goal Davidson made for nearly 6 minutes.
Blue drilled a 3-pointer that pulled the Golden Eagles to 56-54. After two Nik Cochran free throws for Davidson, Jamil Wilson popped in a 3-point, making it a 1-point game with 10 seconds to go. Davidson muffed the inbounds play and Marquette found Blue, who charged down the left side for the game-winner.
Blue scored 16 points to lead Marquette while Wilson ended up with 14.
Cohen had 20 points for Davidson.
Boston schools pull out free condoms over wrapping complaints
Ray Liotta sues skin care company over use of likeness