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.